1) It depends on what specification you are using - but, as this is your first attempt at AS/A-Level exams, you should be able to resit. Maths will be running on the old system still, so you'll definitely be able to resit Maths. (You could also resit Maths AS with the Maths A2 - its quite common, and most will do much better)
2) Yeah, all exams should be in May/June
3) Technically, yes. Normally this is by contacting the universities and going through clearing. That said, if you are doing your AS units now, there shouldn't be an issue with missing the deadline
4) This depends on the course. Most subjects have since moved into a linear 2 year course, where the AS is optional and doesn't impact on your A-level grade, instead of the old system of 1-year AS, 1-year A2. You'll need to find out whether or not Physics and Economics are still using the old system or if they've moved over to the 2-year A-Level.