Ford F150 2004 help can't find what is wrong?

I have a ford 2004 4.6L XLT and it had this knocking noise, so I replaced the motor and when I turn the truck on it shakes when idle, but when I accelerate the shaking stops also it has the check engine light from the old motor and I scanned the new motor and get the code P0351 and P0356.

Added (1). Sorry for my grammar

2006 Ford F150 left turn signal not working, 3rd brake light stays on?

I have a 2006 F150 King Ranch.

All of a sudden my left turn signal stopped working and stays solid. The right signal works fine. The 3rd brake light remains on as well.

When the headlights are turned off, everything functions as normal. When I turn on the headlights is when I have the problems. The signals both work with lights off.

All lights are working.

Could it be the MFS? Short? Fuse?

2006 ford f150 differentials difference and match?

I have a doubt about diferential in my 2006 ford f150 5.4L. Recently my truck was hit while parked on the street and the whole damage was in the rear end diferential so the rear end suspension is totaled and I need to replace it to start using it again. I wanna buy the whole thing but I'm not sure was the difference between all the gear ratios and if they affect the performance. Are all the ford similar trucks a direct fit like example is the expedition diferential a direct fit to my truck or the e 150 van a direct fit to my truck? If you have a real answer to this topic I will really appreciate your help. If you don't have an idea what I'm talking about please save your comment