I did my first 10k after only getting to 6k in training. It's not a strategy that I would recommend, but it does go to show that with another 2 months training you will be better prepared than I was.
If you can fit it in then 3 runs would be better, but I would stick to 30 min for two of them and continue to increase only one of them each week.
After spending ages thinking I wasn't good enough for a club, when I finally found one I wished I had joined sooner. So I would certainly recommend it. The only thing I would be a little cautious of is that most clubs do their longer sessions at the weekend, which may be too much for you at this stage. But check out the clubs web site, drop them an e-mail or give them a call and see whether you would fit in. Tell them what your ability is and see what they say.
My clubs weekend sessions are 2 hours, but there is a lot more emphasis on run/walking than during the weekday sessions, so you wouldn't be expected to run continuously for 2 hours. In fact, we are about to start Race for Life specific training on Saturdays, which might be perfect for you. I know that you aren't local to me, but it gives you an indication of what some clubs do.