The first two are requesting confirmation of a previously agreed to plan or an event that's been taking place recurrently in the past and that might or might not continue this upcoming weekend. The last two sound more like requests and not confirmation. I'd personally use the third one with friends because it sounds funner (not funnier though).

all right

All are correct. The first two are questions which ask for confirmation of plans already made. The third is a suggestion. The fourth is a request.

They are all correct. SHALL is hardly ever used any more, at least in the US. It may be different in the UK. The others are totally natural.