Like many foreign founders in SF, I've become a bit of an expert on immigration, so I think I can answer all these for you. However, I would say that no matter what, you should talk to a good immigration lawyer. Contact me privately and I can intro you.
Firstly, to clarify the process. You can actually prepare the docs and apply anytime, its just that there is a quota of 65,000 (+ 20000 extra if you have a Masters degree), and its done on a first-come first-serve basis. For the past few years, the visas haven't run out until after October, so you can really apply anytime.
OK, so your questions:
1) Interviews are a crap shoot, so you should apply to lots of companies. More than 10 definitely. February is not too late. If they're going to bring you over on a visa, than its likely that you'll do a few phone interviews, then be flown over for a full day of interviews.
2) With a job offer, you'll almost certainly get a H1B, so long as you apply in time. You'll need to have a relevant degree and not have any criminal convictions, but otherwise it should all be fine. When these fail, its typically because the company or their lawyers made an error or got busy. I've heard of people who got screwed because the visa person at their company was incompetent or too busy, and didn't get the H1B in before they ran out, or made silly mistakes. If possible, be involved in the process (ask for ETAs, offer to help, get on conference calls with the lawyers, etc).
3) There is a lot of lore around this, with people saying that you have 10 days, or a month, or whatever to get out of the country. The thing you want to avoid is being "out of status". If you are out of status for 180 days, you might be kicked out of the country for 3 years. Other than that, there are no hard-and-fast rules, and everybody knows it takes time to get a job.
If you do leave the country, you'll still be on your H1B, and so won't be subject to the caps when you get your next job, which makes it all much easier.
FWIW, I misunderstood some rules when starting CircleCi, and had to get a job quickly: I was able to get one in 5 days. If you're an engineer, there's a massive need for you in SF/SV, so you won't have any problem finding a job on a short schedule like that.
A final thing to note is that H1Bs aren't the only option. There are tons of visas that might work for you depending on where you're from, your qualifications, the company you're applying to, etc. Look into the L1, O1 and J1, and to any visas that apply to your country of origin (eg Australians look at E3 visas).
Happy to answer any more questions, and feel free to reach out to me privately at paul@circleci.com.
And we are hiring, see: http://news.ycombinator.com/item?id=5151422. Please apply!