How do I file 2015 taxes for F-1 OPT till Sept 30, 2015 to H-1B from Oct 1, 2015?

You are a nonresident alien for all of 2015, because you do not satisfy the Substantial Presence Test for 2015. Time on F1 is as an "exempt individual" (exempt from the Substantial Presence Test) unless you've been an exempt individual for some part of at least 5 previous calendar years, which you haven't if you've only been to the US in 2012 (assuming you haven't been to the US as a student or intern before). The non-F1 time in 2015 is too short to satisfy the Substantial Presence Test. So you would use form 1040NR / 1040NR-EZ. You also need to file form 8843 (which you should have also filed in previous years) because you have time as an "exempt individual" this year.

FICA tax (Social Security and Medicare tax) is generally not relevant for the tax return (except for the rare case where you pay Social Security tax over the limit due to having more than one job, which is not relevant here). Withholding FICA tax is the employer's responsibility. There is nothing you can do by yourself to pay it. The employer is responsible for paying the taxes to the government, and if they realize their mistake and pay later, they could deduct it from your future pay.

I'm not really sure whether bank bonuses are taxed for nonresidents.

You could choose to use the First-Year Choice and become dual-status (resident for the H1b part of the year). However, the process is really complicated and there generally isn't a benefit to being dual-status compared to being nonresident the whole year, unless you're married in which case you could then also choose to become resident the entire year, which may give some benefits.

Mainstream tax preparation services generally do not know how to deal with nonresident aliens. If you go to them they will likely file for you as a resident alien which is wrong.