i have read this post and other posts. you suggested to book to next station pass Prague to overcome the issue with the website
In case you ok overpaying for your ticket (=buying everything via MAV ticket counter at full fare price when you already in Hungary), then you can purchase it for the carriages with decent arrival time to Prague (6:43am)
since it arrive Prague too early 4am, can I go to the next station, then ride back?
Sure, you can even travel all the way to German Dresden if you want, but the last Czech station will be Decin (arr. 5:58am). Journey back (i.e. Decin-Praha) takes between 1:30 & 2 hours depending on train. Btw, you can stop for a bit in Northern Czech Republic, e.g. train passes quite
picturesque Elbe river valley.
do I need to buy additional ticket to ride back?
Yes, you would still need a ticket back (e.g Decin-Prague or Usti nad Labem-Prague), but those aren't very expensive - with in advance purchase you can buy it for as low as 129/109 CZK
I still would have to wake up ~4am, right?
If you would have the ticket till one of the next stations (e.g. already mentioned Decin or one before it - Usti nad Labem), then no, you can sleep till 5:30-5:45am
If I missed the stop, what would happen?
Well, if you will have ticket till Usti nad Labem/Decin and miss stop in Prague, then nothing will happen, since you have the valid travel documents. But in case you purchase ticket till Prague and don't get off the train there, then you will be the passenger without valid travel document (=penalty). However I doubt that you can really miss the stop, since in couchette/sleeper carriages there is a conductor who knows where passengers get off and can easily wake you up.
is there train arrive Prague in the morning past 6am?
Yes, there is a group of carriages which leaves Budapest with EN 476 "Metropol" train, but then in the middle of the night get "unhooked" and spend couple hours just standing at Pardubice station, while around 5:30am it gets reattached to one of the Czech domestic train and thus arrive to Prague main station at 6:43am (not 4am as rest of the "Metropol" train). Also there is an early morning EuroCity train dep. Budapest 5:25am and arr. to Prague at noon
also, I don't understand name of different train station, BUDAPEST*- vs. Budapest Keleti. if I buy BUDAPEST*- can I board train on any train station? Budapest Keleti- means I can only board train on Keleti station?
BUDAPEST* is just a generic term, which basically means all the Budapest stations (it is there for those who don't know from which station train departs, so by inserting BUDAPEST* system will search from all the station in the city. Trains to Prague have only one stop in Budapest and it's Budapest-Keleti station, you can't board it on any other station. So it doesn't really matter whether you insert BUDAPEST* or Budapest-Keleti.
how do i find out the nearest train station to the hotel I stay?
As was said earlier, trains to Prague depart only from Budapest-Keleti station (which is not very far from the city center and has good transport connection to almost any part of the city)
Please also share you perspective about 1st, and 2nd class seat, sleeper, own compartment, Couchette etc,
Hmm... a bit difficult to do so without knowledge of your preference, but 2nd class seat compartment on the overnight train would look more or less like
this, couchette like
this, sleeper like
this and there is no 1st class carriages in "Metropol" train between Budapest and Prague
I guess own compartment would be more quite, but most expensive. without own compartment, we would have to share with others. I don't mind, but just worried about if it's too much noise.
Cheapest discounted sleeper would cost you 49 euro per person, thus 147euro for 3 passengers (=entire compartment), while in 2nd class seating carriage you can travel for as low as 19 euro