1. At the time of writing, amidst the siege of Mariupol, you can reserve and stay in at least two hotels in the port area of town. (Their names will be withheld for security reasons; but it doesn't take much effort to find out which ones they are.) As a general rule, even in the most wartorn areas of Ukraine, domestically owned hotels have stayed open while a number of the international hotel chains, if internationally owned (rather than franchised to domestic parties), have closed.
2. Although the Ukrainian Armed Forces have asserted that civilians cannot enter or leave the city of Mariupol, that appears to be false; you can, to the north, easily from the port, although you have to pass a Russian checkpoint. Life in central Mariupol remains relatively normal; it is the eastern / western suburbs where the fighting is taking place, as Russian forces seek to gain control over the road between eastern Azov / Donbas and the west (Kherson / Melitopol) that passes through those suburbs.
3. Trains are running virtually all across the country, apart from to and from Crimea, Donetsk and Luhansk. Those services were all cut in 2014; local trains exist in each "breakaway region". Trains in Ukraine are busy (they always were) but the services are usable. The services available include international trains across Ukraine's railway borders; only the services to Moldova have been curtailed. The only substantial restriction upon use of railways is that males of fighting age are not allowed to leave Ukraine using the railways. (Warning; this rule has been selectively applied to foreign males to prevent them from boarding trains.)
4. Most bus networks are also running across Ukraine, as are marshrutkas (Soviet-style minibuses). It is possible to travel by bus to Russia, Ukraine, Poland, Slovakia and Moldova at least; and in the opposite direction. (Nota bene: a western passport holder should not attempt to travel to Belarus or Russia overland without obtaining a visa and, if possible, prior clearance from the Belarussian or Russian authorities of his or her route.)
5. The Gryvna (Ukraine's currency) has actually increased in value during the war, reaching a near- historical high at the time of writing of EUR 1 : GRY 29. The reason for this is the massive budgetary subsidies the USA has paid into Ukraine since the beginning of the war, to peg the Gryvna to the US Dollar (roughly).
6. Telephony and internet remain virtually undisrupted across the entire country, even in areas seeing the most intense fighting.
7. One month into the war, estimates of the number of dead vary from approximately 4,000 (conservative estimates, created by amalgamating the figures of each of the fighting sides of the number of their military dead and adding a conservative neutral third party's estimates of the number of civilian dead) to 14,000 (liberal estimates, created by amalgamating the figures of each of the fighting sides of the number of dead in the other side's military, plus adding each side's estimate of their own number of civilian deaths). This sort of disparity is typical in wars, as each side has an incentive to inflate or deflate certain types of figures to show e.g. (a) the horrendous civilian toll that side is suffering; (b) that side's relative success in killing their opponents at minimum military cost to themselves.
In the Bosnian war, the first modern war in which mass media covered events in real time and hence masses of data could be acquired, the total number of deaths in three and a half years was estimated at between 100,000 (conservative, based upon the methodology set out above) and 250,000 (liberal). One can only ultimately calculate a reasonably precise number of deaths once the war has ended, and an independent neutral evaluator (often an international organisation or internationally funded) counts the number of bodies and/or number of disappeared people and compares those records to pre-war domestic population registers, having regard to regular births, deaths, refugee movements and other events that may skew the attempt to count the number of deaths caused by war.
However it is a common phenomenon of all recent wars that the actual number of dead has turned out to be much closer to conservative measurements than to liberal measurements. That is because double-counting (or multiple-counting) of deaths, whether by journalists, those amassing journalistic data (e.g. Iraq Bodycount) or domestic warring parties, is a common phenomenon in war. The Srebrenica massacre death toll was revised down from an estimate of 14,000 to 8,000 after due study, and that covered a period of less than two weeks in July 1995 in a small town. There is no accurate way therefore of counting the number of dead during a war, unless the set one is counting is extremely small and specific, e.g. dead foreign journalists. Even then there are disputes; several Russian journalists have been killed in the Ukraine conflict but their deaths are often not included in figures for the number of foreign journalists that have died in Ukraine: something that may be revealing about domestic Ukrainian attitudes towards their neighbours.
8. The number of foreign journalists covering the Ukrainian war is at least several thousand, which on some counts may be more than the number of people who have died so far. The reason so many journalists are covering Ukraine, and hence why the Russian invasion of Ukraine has received so much blanket coverage across the world, is surely because travel to and around Ukraine is relatively safe and easy notwithstanding the war.
With so many journalists covering a war proportionate to the war's lethality, over-reporting (or biased reporting), in any direction, is likely, as there is competition between journalists for stories. This author has seen rows of journalists all looking for a single refugee to interview; virtually every genuine refugee has a harrowing story that is individually newsworthy.
One inference we might draw is that mass media coverage of wars, irrespective of whether it is neutral, biased or anything else, keeps the number of deaths down as it keeps the parties better behaved. Therefore even if it biases international political reactions to the conflict, it saves lives to encourage journalists to cover Ukraine. A spike in deaths may result when journalistic fatigue hits and interest in the war diminishes.
9. Most Ukrainian refugees and internally displaced persons are not staying in refugee camps at all, but are staying with friends or family or in private rented accommodation in western Ukraine or in neighbouring countries. The refugee camps are generally closed to public viewing, and this may be because there is nobody in them. Therefore counting the number of refugees and internally displaced persons is extremely difficult, because there is no imagined objective agency such as the United Nation High Commissioner for Refugees with access to the data; refugees are mostly moving privately and hence escaping official figures. Ukrainian authorities seek to make up for this by providing their own estimates, which vary wildly (between 4 million and 10 million) and are subject to substantial inflation in the interests of portraying Ukraine as subject to terrible civilian suffering. The fact is that we may never know how many refugees or internally displaced persons there are, because based upon prior wars the greater majority of them will not come back. All we currently have is anecdotal evidence that refugee movements are substantial. Most of them appear to have been to either western Ukraine or to Poland (where the language is similar to Ukrainian).
Because the refugee crisis has been dealt with mostly privately, it is extremely difficult to provide internationally organised refugee assistance. A lot of the free food offered around the region goes uneaten, because contemporary international management experience of refugee crises is not based upon European wars and in Europe standards are higher, including for refugees. Ukrainian refugees do not want free food of poor quality. Instead they want money. But handing out money begs too many questions: how to detect and prevent fraud and double counting (or worse); how to detect eligible people; how to trace population movements. Conventional refugee crisis work on the part of the international agencies may need rethinking or abolishing altogether and the funds used in a different way.
At the time of writing, there is anecdotal evidence that a substantial number of people who fled Kyiv anticipating its destruction are now returning to their homes because it no longer appears that the city will be razed. However there is no obvious way of counting the number of returnees so it is very hard to estimate the significance of this effect.
10. Because the Ukrainian Armed Forces are organised into a series of independent militias made up of male members of the general public, each financed largely separately by the various oligarchs in (now nominal) control of different parts of the country, nobody really knows how many soldiers are engaged in defending Ukraine. Because the Russian Armed Forces will not release accurate details, nobody really knows how many Russian soldiers are involved in the invasion of Ukraine either. Because the hordes of international journalists tend to be concentrated in the places seeing the least fighting (central Kyiv, L'viv, Dniepropetrovsk and Odessa, to name but a few), it is very difficult to assimilate estimates into round numbers and thereby compare the sizes of the armed forces.
We don't even know which army is bigger, notwithstanding that it might seem intuitively obvious that the Russian army is bigger. We do not know what proportion of the Russian Armed Forces' active troops have been deployed. Low-orbit satellites can count armour. However the reported figures of how much armour each side has deployed vary wildly between estimating Russian armour at 100 per cent to 1200 per cent more. If the world's intelligence agencies have more precise figures, then they aren't telling us.