Are you sure the BB axle isn't bent? Is it wobbly as in physical play/movement possible by wobbling it by hand or just off axis movement when you rotate the cranks?
Not if you're running the freewheel on the back you don't .
A 22T chainring at the front is equivalent to standard 18:15 gearing which is used by pretty much everyone who rides 'proper' trials on stock. Stick with it and you'll get used to it.
One thing to note which is most likely unrelated to the problems you're experiencing is that it doesn't look like the spring is seated properly on the pulley bolt that it's supposed to hook onto.
Try both. You'll probably find on lower things you can give a slight kick to help the forward motion but on higher stuff it tends to be more of a 'deadlift'.
Yeah I ran one for a while but eventually took it off through lack of use. I turned up a custom bolted steel axle for my echo hub and had no problems with it.