Its easy, just takes a bit of practice to get even paint. If you get it wrong its no prob, just let it dry and sand back any bad bits then paint over it again. As long as you get it sanded dull before you put on any primer, you will be fine. If its not sanded enough then the new paint wont stick well. Even if you mess up the whole thing you can just sand it flat again and repaint it.
Put on light coats for 1st coat of primer, also 1st coat of colour and same for laquer. Dont hold can too close or put paint on too thick or will just get runs. Just build up till its all had several coats and looks even. Leave 15-20 mins between coats, do the primer 1 day, leave for good 6-8 hours, do top colour, leave 6-8 hrs, or overnight, then do laquer. Will take upto a week for it all to fully harder up so be carefull till it does cos it will chip and scrape easy till then. And dont polish it for 1-2 weeks, use only water to clean it till then.
I didnt paint the black on my scoot i just use back to black type plastic car bumper cream to moisturise it every month or so.
Ne3ver tried repairing the black plastic. Unless you intended to paint it i think it would be difficult to match in well, prob easier to keep looking on ebay for a 2nd hand panel, you should find a good 1 cheap enough eventually. If you are going to paint the black bits then use araldite or similair to gradually build it upin layers to fill it up then sand it back flat once it dries.
Good luck.