well, before you get back onto that bike, you might change those pedals I'd not want to be clipping in until I had gotten the other issues figured out.
I'd look at bike fit for one thing. Did you get fit to this bike or did you just get it handed to you?
Is all your weight on your hands? That's not good, that would surely cause wobbling.
One thing that will help is just getting used to the bike. Good luck and welcome to TE