(Clearly) Eliminate paint damage

Moin Just bought me a somewhat run down winter car (E81 130I), which I want to freshen up a bit, low budget. After the winter I decide whether it will be a longer term relationship and I invest more. How do I fare best with the clear varnish bursts? Sand on edges and fill up with paint pin? Does this also work on the bumper or do I need a primer? The last photo looks as if the paint has come up. I have already finished this However, even here there is probably only the paint pen, with spray can excrete, due to the temperatures probably at the present time.