Bratislava - St. Petersburg via Ukraine and Moscow

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On MAV-Start website it's stated that return ticket Budapest - Kiev is 76,80 eur, so one way shuold be half of that, considering that now is same discount for one way and return tickets.

If you referring to a map from MAV website (http://www.mav-start.hu/utazas/nemzetkozi/nemzetkozi_index.php), then we would not trust it so easily. Some fares there tend to be out of date - check Budapest-Krakow return (it's not 78, but 90 euro) etc.
Other evidence - last month one of our team members was in Kiev and exactly checked fares for international routes. Kiev-Budapest one way ticket+reservation was just over 800 UAH (exchange rate at that time was 10.5 UAH for 1 euro), means around 75 euro for the whole package, minus reservation and commission we have around 45 euro for the base ticket. That is the reason why we gave you maximum to expect (same thing with Lviv-Budapest). But if we follow strictly tariff tables, then yes, fare should be around 38-40 euro, but we aren't sure about that 5-7 euro difference here - maybe some kind of hidden cost or exchange rate fluctuations. Anyway - you won't pay more than 45 euro, that is for sure   

Just to make sure, this is only for Ukraine - Hungary, not for Hungary - Ukraine?

Yes, in Budapest you can easily buy in advance reservations for both RZD and UZ carriages (Budapest-Moscow and Budapest-Kiev respectively). But in case you want to use Belgrade, Zagreb or Venezia carriages, then same story - sleeper reservation can be bought only after MAV receives info about number of passengers in those carriages (--> means after leaving start destination).
Since usually there are always some seats left in either of carriages, so it is not a problem to buy reservation even an hour before departure or even from conductor already in the carriage.

Well, then I can buy both tickets Budapest - Kiev and Lvov - Budapest already in Budapest, and only sleeper reservation Lvov - Budapest/Belgrade in Lvov, so it will probably be few euros cheaper. And also, I can save few euros if I buy Belgrade - Zahony return ticket, and then in Budapest buy Zahony - Kiev and Lvov - Zahony. That way I can get 60% discount between Budapest and Zahony instead of 50%. I hope conductors will not make some problems with that. I realise that that is legal.

I think that for Budapest - Krakow is written 78 euros because the cheapest one way SparNight ticket is 39 euros (6-berth couchette), so both ways is 2X = 78 euros.

I can save few euros if I buy Belgrade - Zahony return ticket, and then in Budapest buy Zahony - Kiev and Lvov - Zahony. That way I can get 60% discount between Budapest and Zahony instead of 50%. I hope conductors will not make some problems with that. I realise that that is legal.

Yes, it is fully legal. But it will be a little bit vexing, because of the knowledge that ticket from Chop (which is couple km from Zahony) costs like 3 times less (or even more with Lviv-Zahony) for almost same comfort 
Anyway, it is your choice. Option with Beograde-Zahony r/t+Zahony-Kiev+reservation Beograde/Budapest-Kiev sounds reasonable, if you don't want to deal with train changes at the Hungary-Ukraine border.

I think that for Budapest - Krakow is written 78 euros because the cheapest one way SparNight ticket is 39 euros (6-berth couchette), so both ways is 2X = 78 euros.

Hmm... you probably right, they meant SparNight 

Considering variant via Romania, how much will be the cost for ticket Chernovtsi - Bucuresti, and Lvov - Bucuresti?

Lviv-Bucuresti one way ticket cost app. 45 euro, sleeper for UZ carriage 16 euro (2/4), for RZD should be cheaper, but don't know exactly.
Chernivtsi-Bucuresti one way ticket cost app. 32 euro, sleeper UZ - 13 euro (2/4), same story with RZD sleeper.

And how much is cost for sleeper Zilina - Lvov RZD coach, Bratislava - Lvov UZ coach, Lvov - Moscow (RZD adn UZ), Kiev - Zilina RZD coach and Kiev - Bratislava UZ coach?

Kiev-Bratislava (24 euro, UZ 2/3), Kiev-Zilina (19 euro, RZD, 2/3), Lviv-Zilina (15 euro, RZD, 2/3), Bratislava-Lviv (19 euro, UZ, 2/3)
Lviv-Moscow 2/4, 20 euro for UZ carriages and around 60 euro for RZD carriages (both in case of East-West tariff) or a bit more if 2/3 RIC carriages used.
Also to remind you - on the route Lviv-Moscow the only train having RZD carriages is "Tisza" (#15/16), trains #74 and #142 served by UZ.

How much in advance domestic tickets in Ukraine has to be bought to secure kupe place, or at least platskart? I plan to stay in Lvov only 3 days (2 nights), and then move to Odesa by night train. Will it be too late? It's late July. I will also buy tickets Odesa - Simferopol, and Simferopol - Kiev in already in Lvov to secure place. Also, is it possible to buy ticket Kiev - Budapest in Budapest already, and then buy only reservation in Kiev?

Lviv-Odesa: generally, you will not have problems. Even if all the tickets for train #26 will be sold out (quite usual thing during summer), then there are still additional train #228 Lviv-Odesa, as well as regular #136 Chernivtsi/Ivano-Frankivsk-Odesa and #107 Uzghorod-Odesa. Just checked - even for today there are some places left.
Simferopol - Kiev route during summer served by dozen of trains, so no problems there. Purchase of tickets for Odesa - Simferopol couple day in advance should be fine too.

is it possible to buy ticket Kiev - Budapest in Budapest already, and then buy only reservation in Kiev?

Yes, why not.

I checked at http://www.e-kvytok.com.ua, for 3 days ahead, and there are no places left available for any train Lvov - Odesa. Is it only internet availability, and there are some tickets left only to buy at station?

Probably yes, there are suppose to be some kind of station reservation (available for sale only in Lviv). Another most possible explanation - Friday and weekend - as you can guess - busiest time. For Monday 12/07 there are still almost hundred places left.
If you worry that much:
1) there are two direct everyday trains Lviv-Kherson, they go via small station Kolosivka. From there you can catch multiple suburban trains to Odesa (between 2 to 3 hours)
2) catch any train from Lviv to Zhmerinka. The station can be considered as main gate to Odesa. All the trains from West and North of the country transit the station, so from there you will definitely find some places, especially 3 days in advance.
3) If you for 100% sure about your date of departure - buy ticket from e-kvytok. Commission won't be that high - between 15 and 30 UAH (depending on type of carriage and train).

We came back from Ukraine. Had no problems buying tickets for domestic train, except the language barrier, but I used some of my russian, learned years ago. 

We payed 20 euros for UZ 2/3 carriage Budapest-Lviv, directly to provodnik, but for return we bought it at the station it was 32 euros (it was 19 euros reservation, and 13 euros of taxes). So, it's better to get it directly from provodnik if you go from Ukraine back.

We came back from Ukraine. Had no problems buying tickets for domestic train, except the language barrier, but I used some of my russian, learned years ago.

Good to hear. Hope you didn't melt under Ukrainian sun 

We payed 20 euros for UZ 2/3 carriage Budapest-Lviv, directly to provodnik

with receipt or "unofficially"?

but for return we bought it at the station it was 32 euros (it was 19 euros reservation, and 13 euros of taxes)

Hmm... really strange. It is possible to believe that cashiers approximated reservation toward bigger sum and took 19 instead of 18 euro, but "13 euro of taxes" sounds extremely unreasonable 
It's never been more than 3 euro, so we don't even know what to say. Can you scan/make a photo of the reservation and post it here, thus we can take a look?

Almost got melt. 

We payed unofficially, no receipt.

Well, we saw that commission for international ticket/reservation is 40 UAH, and there were some more few smaller "taxes", written on reservation. But that was maybe because we bought Lviv-Budapest reservation in Kiev. And, also, the cashier needed 25 minutes to issue the ticket. I just called my friend who kept the the reservation, but he couldn't find it. He probably trown it away.  If he find's it, I'll post it.

we saw that commission for international ticket/reservation is 40 UAH

Exactly, it used to be 45 UAH, now 40 UAH. It is standard commission for purchase of international sleeper reservations on UZ.

But that was maybe because we bought Lviv-Budapest reservation in Kiev.

No, I doubt it. In Ukraine fare doesn't depend on place or date of ticket purchase.

And, also, the cashier needed 25 minutes to issue the ticket.

Yepp, it is very well known problem since tickets issued by hand + most of the cashiers at international counters in Ukraine aren't very professional, thus having troubles when they need to issue ticket/reservation from station other than there own.

If he find's it, I'll post it.

Ok, it's simply interesting what for you payed almost 10 extra euro.

Anyway, sorry for misleading you with reservation price. All the official docs show 18 euro for Lviv-Budapest in UZ carriage + standard app. 3 euro (40 UAH) commission.