Your employer has no legal obligation to hold your job beyond the 12 weeks of FMLA. On week 13, day 1, he can legally let you go if you are not able to return, unless a legally binding and enforceable CBA or contract says otherwise. I am not saying you WILL be let go - I am saying you CAN be let go. Not all or even most employers will do so, but they legally CAN.
While only someone who has read your STD policy can say for certain, I can tell you that in 30 years of administering employer-sponsored benefits I have yet to see an STD policy where the benefits stop when employment does. The overwhelming likelihood is that you will be able to continue to receive benefits for the open claim until either your condition improves to the point where you are no longer eligible, or the number weeks on the policy has been exceeded.
Only your employer can say whether your medical coverage will continue or not. You WILL be eligible for COBRA.