I would not wear a trench coat with baggy tracksuits.....Jeans, chinos or trousers would be okay.
As for the second question...I don't have any opinion at all....
A trench coat is quite smart, even if its casual chic. Jeans are best, chinos are OK if they´re not same color as the trench coat!
baggy tracksuit is sporty, even if it´s sporty cool, your coat/top needs to be as well, or at least a leather jacket.
We are all free to wear whatever we want. Please post a pic of the trench/tracksuit combo. It never crossed my mind to combine the two but that's me. Why not wear the handkerchief on your wrist? An unused one by preference
1. I think trench coats are inherently dressy - I personally wouldn't wear it with a baggy tracksuit (but to each their own, and I guess it could depend on the tracksuit). Out of those options, I think it would look great with a really simple pair of skinny jeans! If you want to find something to wear with baggy tracksuit pants, you could try a slightly oversized jumper (Alexander Wang-esque style)?
2. That's never actually crossed my mind! But why not! Would love to see a pic
since learning you are a dude, i would give a resounding NO to the "neckerchief". no to the tracksuit with a trench, but if you really want better opinions i would suggest posting a pic tbh