2) Yes, in principle, though (a) it complicated taxes and (b) none have ever taken me up on the offer. You could go to a factor to do it for you though.
3) Unless it's a huge difference, no.
When I started at RBS in 2008, having escaped Lehman Brothers just in time, I was glad that I had been switched to weekly invoicing (without being asked) since RBS' share price halved live while I watched in the first week and I wasn't sure that RBS would be alive to pay me in week 2!