Clutch is not adjusted properly, pull the clutch horizontal arm further up the clutch cable.
Finer adjustments with the flower nut under right side cover.
Very tight, like the motor and bicycle are one solid hunk of metal, the slightest push or pull to the motor head should result in the rest of the bike moving with it.
Big problem is the stud holes in the motor itself, they can be rather weak and that ends up in stripped threads, picking up a helicoil kit in the size your mounting studs are will be very helpful in the long run. You'll be able to torque them down untill it's as solid as a rock. Also head out to your local hardware store for replacement bolts/studs in the highest grade they have (8.8 is most commonly found in Lowe's and home depot) so you'll be able to torque it without stripping the bolt too, get a handful of matching nuts and lock washers, blue threadlock if you are feeling amped (the store probably has a helicoil set anyways, 2 turds 1 bone)
Double check to make sure you are properly mounting the engine with the required spacer on the rear and that your seating good on the front. If the front mount isn't meeting quite flush with the tube the maybe a slight modification would be in order, use a large rounded file to file the engine front mount to match the angle of the tube a bit better. I had to use an angle grinder on mine to match the almost 2 inch tube my bike has, a file would've taken years...
You can remove a hefty portion of that mount area without risk of harming the motor, it's there for show and not to much else. Helicoil those stud holes definitely.
After an afternoons worth of work, you'll have a very strong engine mount, you really can't have flex otherwise the chain will begin wearing badly, even breaking, or slipping off the rear sprocket. The motor will be subjected to more vibration rather than sending it into your hands like a properly mounted motor should, which just causes the engine to break down faster...
Good luck, welcome to the very painful world of bicycle motors. Once you get used to the 80 or 90 things that go wrong on a roughly bi-monthly basis you'll enjoy it.
