I don't know this turntable, but I have some comments from general principles.
I would set the stylus pressure to two grams, just as a starting point. You could try varying it up and down by half a gram in quarter gram incrememts to see if a different setting improves the sound. I wouldn't want to play my records at 3 grams or higher (fearing record wear), and very few cartridges will track decently below one and a half grams.
It seems the speed selector rake needs a repositioning adjustment. See if there is a screw somewhere that might allow you to reposition the rake so that it still serves to change speeds but doesn't rub during play. In the limit, if there is no screw, you might just have to bend it gently by hand.
This may also eliminate the grinding. If not, you might allow the grinding if it occurs only during start up. Your description doesn't say that the grinding persists after start up. Also, I'm not sure what you're referring to when you say "float." Is this an object or a direction relative to the spring loading? If the turntable is very old, it is possible the spring has deteriorated and is too loose. If so, one remedy would be to shorten it by very carefully by cutting it shorter. The spring loading was probably intended to absorb/reduce motor vibration, so you don't want to defeat its function completely.
To a certain degree, Kehut's comments are good advice. This unit may not have been very good when new, and whether you want to keep it in its current state is quite problematic. I hope you didn't pay a lot for it. I personally would rather spend some money on a better unit instead of spending time and money fixing this one and replacing its cartridge. Good luck.
