Disclaimer: I am a music nerd. I took a great deal of classwork in the field when I was shooting towards a music performance degree. I wound up getting my B.A. in elementary education, but the musical knowledge has stuck with me.
Some general notes on orchestration (I only just discovered this thread, and my husband is currently playing a noisy video game, so I haven't actually listened to the thing yet):
Eb clarinet is usually either a sopranino clarinet or an alto clarinet. Contrabass clarinet is also in Eb, but it's huuuuuge. Bb applies to the standard (soprano) and bass clarinets. You also have a lot of oddball-keyed clarinets; the most commonly used is A, which is similar to the standard Bb in pitch and timre. Its existence is mostly due to the classical age writing music for orchestras that had a lot of sharps. Natural key signatures of sharps combined with instruments pitched to the flat side of things makes for horrendously evil key signatures and double sharps and nigh-Lovecraftian musical notation.
Same sort of deal with the C trumpet; it's just easier to handle a high-sharps key signature.
Basically, when you have an instrument that's pitched with flats "built into it", you have to add extra sharps to the instrument's music in order to balance them out. So if you have a Bb trumpet, that's an instrument with two flats built into it. If the concert-pitched instruments (that's the C instruments to the laymen) are playing in the key of C, no sharps or flats, then the transposed parts for the trumpet will be in the key of D. That's two sharps to cancel out the two flats built into the instrument. On the flip side, an A clarinet will have three sharps built into it, so a piece in the key of C would have to be transposed into Eb for it to balance out correctly.
Why are instruments pitched this way at all? It comes down to playability. By pitching the different instruments, you get a standardization of fingerings within the different families. Saxophones flip back and forth between Bb and Eb, but on all different types of sax (sopranino, soprano, alto, tenor, baritone, bass) the fingerings for different notes are exactly the same. Oh, and play a G on a saxophone? It's pretty much identical to how you finger one on a flute, in spite of the fact that the instruments look wildly different. This standardization makes it very, very easy to learn to play new instruments in the same family.
I'm not familiar with Musescore; I use Finale for my writing. It's a nice program. You can have the score switch back and forth between concert pitch and natural pitch. It's a heck of a lot easier to enter parts when you don't have to try and transpose them in your head.
Changing the pitch of a timpani mid-performance is doable, but it depends heavily on the level of the orchestra. It's not something I'd expect a high school player to be able to do, but a good college player could probably do it, and a professional orchestra member expects this sort of thing as a matter of course.