Hi sparklegem, nice to see you again!
1) Yes, a Yeerk can give control to its host if it wishes. Chapman is given the control to talk for himself in #2, but I think the best example is in Visser
, when Eva was given control over one of her eyes for a long period of time, to see what she'd do. So not only can a Yeerk give control, but they can also give control to specific parts
of the host back to them as well.
I'm sure there are other examples, but I can't think of any that don't involve a fight for control between the host and Yeerk. Mr. Tidwell (#29) is a good example because their relationship is almost symbiotic in a way, though we don't know how much control the real Tidwell really gets on a day-to-day basis when Illim (his Yeerk) is in.
As for Cassie as a Yeerk, it could simply be that it was a new morph and couldn't fight against the controlling instinct of a Yeerk, and wasn't able to give any control away due inexperience.
2) There is a lot of debate over this amongst fans, as the series is pretty inconsistent at times. Officially though, the rules are that all injuries are healed with morphing, even the morpher's original body. The Megamorphs #2 bit with Tobias's broken wing is a known KASU, because K.A forgot her own rule and tried to solve it by coming up with a time traveling glitch (I believe it's listed in the book pages under 'Missions' up top).
Hope that helped!