The deck problem. Look under the right side of the mower and find the deck brake arm that touches the spindle pulley. follow that arm back under the mower, and the other end will have a roller on it. That roller contacts a idler arm bracket, and when that bracket pivots to the rear when the engagement cable pulls it back. Now look where that roller contacts the idler arm. You may see what looks like a notch worn into the bracket. That notch will act like a detent and prevent the deck from disengaging.
I have found the only way to fix the issue for any length of time is to replace both the brake arm and the idler arm. If you don't replace the brake arm, it will wear a new notch into the idler arm before the end of the summer.
The brake problem could be due to grease contamination of the brake pads, The brake is located under the right side of the tranny in front of the axle. There is also a nut that holds a flat piece of metal with a slight twist were that nut is. That is the adjustment nut for the brakes. You may want to play with that turning it in slightly to see if that helps the brakes..
The last thing with the shifting. Does the mower shift OK when the engine isn't running. If the shift problem goes away then most likely the belt isn't disengaging all the way. The rod that goes from the clutch/brake pedal to the idler tension arm should have a way to turn the rod to allow for the belt to disengage further. If the shift problem is present even when the mower is off, then you probably have a linkage binding problem, and may need to spray some penetrating oil around where the shift rod goes into the tranny.