33 Countries not including micro-states, here is a summary map
https://www.interrail.eu/content/dam/pdfs/Interrail%20map%202022.pdf
This gives a rough idea of the places and routes covered but is not at all comprehensive or any indication of service level, some lines may have 100 trains a day, others one a week if that.
Night trains:
3 basic categories:
Seat; self explanatory, can be in open carriage or compartments of 6, shared with whomever is in the other seats.
Couchettes: compartment of (usually 6 or 4) berths in 2 bunks, shared unless you or your group buy the whole compartment.
Sleepers: compartment with one bunk of 2 or sometimes 3, will usually have wash basin, some deluxe have toilet and shower as well, can be shared with travelling companion or stranger or bought as solo occupancy for one person or couple for an extra fee.
Main night operator across Europe is now Austrian state operator Obb’s Nightjet, their website gives good details of the various accommodation available https://www.nightjet.com/en/#/home They also list some of the Euronight services through Eastern Europe.
Other sleeper services are offered in Italy, UK, Sweden, Norway, Finland and no doubt some others I have forgot to mention.
I would suggest you revise your budget unless you are planning very basic hostel style accommodation. To do 12 countries with a suitable pass over 16 days (4 stays of 4 nights), plus food and tourist spend will need a very minimum of 2500 but I would be budgeting at least 3500 euro for safety. I would hope to bring back up to 1000 euro, but that would be unlikely.
2 * 15day in 2 months flexi passes would be from 740 to 1000 euros depending on age. Accom needs a budget of 100 euro per night for B&B. General dining from 20 to 40 euro pp and tourism spending will be a few hundred euros.
It all depends on how you intend to travel-obviously. IF you are young/studentsy bekpekkers and comfy with that it can be done for less-but then do not expect Finnish style comforts at all. You probably know that FI -with Scandinavia-will be highest priced in EUR-former ´East´EUR is and remains cheapest.
But if you ask about private WC in train compartmts it does not look you are willing to compromise a lot-this will be VERY rare and hence inquire a huge surcharge-in fact most trains will not have it.
Best general info+pix is on seat61com-incl many descriptions about train routes-it is not aimed at passholders and aims Brits wishing to go overland from that island to all EUR countries-so you can pick out the sectors that you could use.
Your budget is way off unless you stay in hostels or use AirBnb apartments and self cater.I’d allow 200 euros per day for hotel and a decent meal leaving money for a light lunch and sightseeing. If going to Scandinavia you’ll need 300 euros a day. Then add the cost of the passes and any supplements for high speed trains. I’d avoid night trains as it is difficult to sleep on them and the compartments are tiny! The community can give you a lot of advice but we need a lot more detail. Plan using the national carriers sites and read the sections on this site about reservations