I hope this might be of some help.
If you have a standard TP 1600 Remtec engine then the chances are you will have a 009 dizzy. or did you buy a complete engine ?
It sounds like you have an air leak, this will be easy to check, you will need some easy start or simular liquid, must be very flamable! you will need to tick the engine over say around 2k, so set it up so you are happy it will stay around that revs, then take your easy start and i would check around the inlet manifolds all rubber joiners ...do not miss any part out !, including around the J clip!, the second place to check is the throttle linkage on the carb, make sure you spray it in the area the linkage enters the carb, then check the base of the carb, every place you spray make sure you are happy you have sprayed enough and covered the area well, also spray the ends of the manifolds, the part where they are bolted to the head, what you will be listening out for is ANY and i mean ANY change in revs, because you will be using a very flamable liquid if you have an air leak in ANY of the area's you have sprayed you will obtain a difference in revs. as soon as you hear your change you have found your problem, or at least one of your problems, you will never be able to tune an engine with an air leak, please post what carb you are running ?????, also please post what dizzy you are running ?????, you will do your air leak checks one at a time. also did you have any back firing ????,
Engine running hot is usually because it is running lean, chances are you will not be able to correct this untill you have corrected the air leak problem,
If you are running an 009 dizzy these do not run as advanced as they should, thus it will make the engine run hot, advance will not kick in untill around 1200 revs,
and i think the carb you will have on your engine might be a Bocar.
As for your vibration, it could be as simple as your gearbox mounts! check for any wear, check your engine is bolted up tight to your gearbox ! hope this helps with abit more info on what your running will be able to give more advance advice.
Danny.