TSB issue for sure. My car did the exact same thing and was fixed by Ford under warranty. The symptoms you describe are exactly what my car was doing, and the misfire was significant enough that it could be felt when under partial throttle or in gear and coasting to a stop. I pulled the codes myself and noted several misfire codes. I accidentally cleared them before going to Ford, but they took my word for it and performed the TSB for me.
As for warranty coverage, the powertrain warranty typically covers "oiled" parts. So anything the gets covered in oil, such as engine internals (crank, pistons, cams, etc), transmission and rear differential. Electrical items may or may not be covered...I have never read the fine print on the powertrain warranty. My service was performed under the bumper to bumper when my car had about 7k miles (but was 2yrs old). My warranty has since expired due to time on my 2012.
Cheers, and good luck!