As others said I'd also set up hotels or flats before going if it is their first trip there. Flats are cheaper and you can get decent ones for good prices. Transportation is excellent using the micro bus and everything else they have.

Z

2) You can also arrive in Odessa.  I think there may be one more place to arrive as well.

3) If they were going during tourist season they'd need to  make reservations beforehand.  October isn't tourist season though.  If they want to chance it, they can try to negotiate on the spot.  Personally, I try not to leave anything to chance.  Last thing I want is to be running around a foreign city looking for a hotel to take me in.

As far as comparing to Russia, I can't help you there.  Hopefully, someone else can provide you some info on that.

Registration is no longer required, but it they stay at a hotel, the hotel will register them as a convenience.  Your travellers have nothing to worry about there.  

If they are city hopping, they might want to arrange some transportation with a travel agency in Ukraine.  They can then set up tour guides, cars with drivers, translators, etc. beforehand.  If they are travelling by train, they can get the tickets purchased beforehand.

If they travel by train, they should reserve private coaches for themselves.  Coaches are reserved for 2 to 4 people.  If they want to travel alone, they will need to buy the other tickets for the coach.  They can buy children's tickets to save themselves some money.  I also brought a little bit of clothesline in my suitcase, so I could tie the door shut when I slept.  My wife and I weren't really disturbed after the train got started, but it was a nice precaution.

Hope this helps.