Je gère le stress en regardant mon film ou ma série préféré toute en mangeant du pop-corn.

Ouh... That is a tough one ! Those rules aren't my strong suit, I hope Mr Elephant will come and check after me :D

So... in this sentence the adjective "préféré" is shared by two names, "film" and "série", which are respectively masculine and feminine. In such cases the match of the adjective is determined as follows :
- when nouns are connected with "ou", the last name wins
- when nouns are connected with "et", if there is one masculine noun, masculine wins

Let's put those rules in action, those are legit :
"en regardant ma série ou mon film préféré"
"en regardant mon film ou ma série préférée"
"en regardant mon film et ma série préféré"
"en regardant mon film préféré ou ma série préférée"

"tout en" is OK, but not needed. Furthermore we would rather use this expression when it is important to emphasise that we really do B in the meantime that we do A.

Parfois, je peux aussi dessiner ou lire un livre.

Your sentence is OK, but adding "aussi" allows to connect to the previous sentence and make it explicit that we are not suddenly discussing your general abilities (je peux ~ I can), but still discussing your ways to deal with stress.