| The whining sounds like a bad PS pump. The problem of it wants to turn on its own sounds like a caster related problem. The wheel is there in the wheel well, it is not supposed to move forward or backward, it turns left and right when you want to turn, this is toe in and toe out kind of thing, when you go over bumps in the road, this is a camber type thing, but caster should not allow the wheels to go forward or backward, I think you have a tension rod bushing worn. It should be a rod that goes from the lower swing arm (control arm) towards the front bumper and connect the the frame. You may actually see this motion if you let a friend put it in drive with the brake on, release the brake, apply the brake once the car starts to move, go in reverse with the brake on, release the brake, hit the brake again when the car starts to move, do this a few times and you may notice one front wheel and tire move forwards or backwards.
The transmission shifting issues will need a flush from a Quicky Lube type place through the dip stick hole while the engine is running OR you can do three---three quart fluid changes with OEM Honda fluid, running the engine for several minutes between drain and refills, ask the lube shop if they have OEM Honda fluid or can you bring your own. Unfortunetly a Honda of your age does not have a servicable filter or an accessible valve body, so if the flush does not help then its tranny time, inspect all the motor / tranny mounts for being broken also. | 
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