It's pronounced "shch" (as in Khrushchev), right?
Kind of. But in Russian there is a single letter for it. Latin script should not be used for Slavic languages 
Polish Cyrylic alphabet probably would need letters not used from centuries like https://en.wikipedia.org/wiki/Yus ...
Of course! That is the beauty of it! Get back the Yuses (I guess, both the lesser and the major, and the ioted forms of it). Cyril and Methodius have thought about all of that
Believe me, I tried to use Polish Cyrylic alphabet with yus and writing that letter is pain in the ass. Handwriting is much slower because of that. I prefer using Latin alphabet on everyday use.
Just invent a modern cursive version of it, for gods' sake. I mean, not that any of those letters are easy to print.
