1. You definitely don't need to form an LLC. I'm still a sole proprietor all this time and it's working out fine.
2. Personally, I'd hold back 35%+ of your income for taxes and expect to pay taxes every quarter.
3. 2 months of savings seems really low. People are wired different but I know a lot of people (myself included) who can't function with less than 6 months of runway when being self employed. It's not fun being in a position to take on low quality work because you absolutely need it.
4. Billing style really depends on the job you're doing. A lot of my work is billed hourly due to the nature of what I'm asked to do.