WE have the Healthy Care chair, too, but ours is about 5 years old. The wheels don't lock by themselves, but Boo likes to sneak under it and lock them. Our tray has occasionally not engaged properly, so I have gotten in the habit of just forcing it and checking it before I let go. None of our sippy cups fit in the cupholders either, which does annoy me, but Boo throws his cup on the floor or at me so often and THAT bothers me more.
I agree about the portable booster- we have one I think is also FP and it's great because it attaches to the dining seats, has a seatbelt, folds easily to take with us, and has it's own dishwasher-able tray. I'd ask customer service to allow you to switch to that one.
Mama to DS1 Punkin (2/04) and DS2 Boo (1/09)