Hmmmm....

You installed the new trans & everything seems to work fine... then the NEW starter catches fire. You install another starter & you have a sluggish motor & a squeeling noise!

The starter catching fire when driving down the street seems to be the key. Sounds like the starter drive never fully disengaged ... though it seems like you would have been aware if that had happened. I can't imagine a starter catching fire for no apparent reason.

Assumption #1
The car ran well before installing the new trans & starter.
Assumption #2
You reinstalled the trans yourself & assume the trans operated correctly. Do you have a manual valve body (no vacuum modulator required) & what kind of convertor did you install?

The squeeling noise & sluggish motor remains a mystery for now ... However, I advise you not to drive it until the source is determined.