1. it doesn't matter (w/ or w/out piano)
2. yes, I played the Brahms Sonata (e-minor) and a movement of the Shostakovich sonata, and anyway I started to learn the Shostakovich 1st cello concerto. My most difficult piece was my friend's cello sonata, but I think you don't know that piece

3. What do you mean? Write a private message about your ideas. (Anyway I think, yes)
4. Hm.. I don't know. I can make pppppp and ffffff on the cello, I like plucky things in the music. I am flexible in the styles, I like to play modern, and romantic pieces too (less classical)
5. Long bows (I can play it, but I don't like them.), and of course high notes. In my last piece, I wrote myself a Bb, the third above the staff, but it was a really long (27 sec.) note, so it's easy to play. But if you write something virtuoso, it's difficult, of course.
But I think, I can learn everything. I won't choose the easiest one. I will choose the best piece.
You can write anything, just have your own borders. For example, don't write below C... Use the cello's possibilities, the range, and the effects too. Think about the effects, be creative! I won't give you examples, I can't help you

BUT, write a playable and a "celloish" piece!
Come on!

Good luck!