Taking over a platoon where the previous PL was fired. Any tips on how to improve PT, morale, and unit cohesion? Thank you.

Don't try and be something your not, don't try and be different, just be a leader, open, honest. Accept you will make mistakes as will your subordinates, Accept you are not all knowing. When time and situation allow, listen fully before speaking, consider all options to include your subordinates fully before acting. When warranted accept what your doing is not working and try something different, even if that means doing it in a way suggested and rejected earlier.
Be consistent in both praise and rebuke. Praise in public often , complain up only, rebuke or counsel in privet.
Dont focus or let them focus on past issues, speak on it once , be done with and move on. You cant change what happened, only effect what happens now.

Lead from the from the front and gain their trust and respect, the results you are looking for will soon follow.

It is a great thing to see a young officer asking for help. That says a lot about the type of officer you will become.