I think it's a nice trip you have planned. All three cities are very nice.

You might find that you don't have time to do all the things you have planned but you can adjust along the way.
You have probably squeezed to much into the Vienna part, if you want to save a little time you could visit the Belvedere Castle instead of Schönbrunn.
Add : just noticed you have both castles on your list - then consider leaving out Schönbrunn due to time restrains.
Also take a little time to relax, stroll around in each city, sit in a cafe etc.

No problem managing with English in either place in my opinion.

I don't know the hotels mentioned, so can't help you there.
In Prague, I most often stay in tbe Hilton Old City - very centrally located, very nice hotel and easy access to/from airport.
In Budapest I like the Hilton Budapest (Castle) but it is not very centrally located. I like the area though, fantastic views from Danube rooms - next to Fishermans Bastion, the church and close to the castle.

All three cities have very good public transport - look into buying day tickets, multiple day tickets or such.