Can't answer your other questions, but as long as you've got solid proof of your cohabitation w/your partner - things like bank statements with your joint address, utility bills, etc. - the visa shouldn't be too big a deal after 4 years. You could go for the HSMP, but the Unmarried Partner sounds like it'd be the surest bet.
Another thought, if you've been working here for 4 years, do you qualify for ILR - permanent residency - based on work permit sponsorship? I'd suggest asking in the Visa section.