Alright

a) The theme music is midi. If your original computer had midi built into the sound card or different soundfonts then the instruments would sound slightly different, but the notes and tempo would be the same. The only way you could reproduce would be to use your original computer.

b) There have always been bugs in Theme Hospital, perhaps you are playing more thoroughly now and notice them more. Some of the bugs may have been different between the windows and dos versions.

c) I think the speed is the same as long as you had a sufficiently fast computer now and had a fast computer then - though it is running through dosbox so there might be some variation in timing because of imperfect emulation. There are speeds slower than normal which are good to use when setting up your initial hosptial.

I think the Gog experience is relatively authentic, at least the best that can be done with modern hardware.

There is also the open source engine replacement corsix-th that you can try with the GOG version. It's not yet nearly as polished as the original game, but people are still working on making it better.

Consider what TheCycoOne said. If you disagree with his comments, it is certainly your right not to purchase any more games from here. (I'm not trying to be rude, I'm just being matter-of-fact. :)

The music sound slightly different because the gog-version is the dosinstall of the game. The music sounded a bit different from the dosinstall to the windowsinstall. I had a bit of issue with it (having OCD and all..) but after a while I got used to it as well.

The stuck bugs and speedproblem is solveable if you fiddle a bit with the game configfile. Try to reduce the cpu cycles of the game to 10 000 or less.

Sound can be fixed with the file/guide in this thread:
http://www.gog.com/en/forum/theme_hospital/changing_the_sound

It's less that the DOS version is different and more that GOG configured it differently. Have a look at the thread sai linked to. :) See above. Games from this period supported many different sound cards, GOG just happens to have configured it for adlib music instead of general MIDI.