That "shaking around" when you're focusing is probably the mount not being stable enough.
You'll always get a little bumping when you manually focus because you're making contact with the scope through the focuser so you cause vibration. A better (smoother) focuser will help, as will a more sturdy mount. An electronic focuser will do away with the wobbles altogether but that's getting costly and unnecessary for your purposes.
F4's even shorter than my Skywatcher (F5), so collimation will prove even more critical and harder to keep. You'll need to learn how to do it. I dare say it's causing your jupiter probs. That and maybe some poor seeing?
