It looks like I might be moving into an apartment with a 1st floor balcony on the east side of my building. The street outside the balcony has lots of tall trees as well, so there's only direct sunlight for a short time each day, and lots of partial shade for most of the day. I was wondering whether it is possible to grow heat and sun-loving vegetable crops on this balcony if I hang up lots of reflective material around it- in particular, I was thinking of shiny mylar film which is extremely reflective, like a mirror basically. Can having reflective film right next to a container growing tomatoes or peppers allow said plant to grow in a shady place?

Yes, I know it is more reasonable to grow things that fit my climate + conditions, but these are the plants I love the most, so if it were possible to grow these, then that is what I would chose to grow.

If it's a matter of enjoying your plants, find a different home so you aren't miserable come summer. Otherwise, stick with shade-loving plants. Sorry. :(

Reflective material may take the place of sunlight in the growing season, but it can also burn if hit directly by hot sunlight. This too can happen in winter when combined with wind. Wind is the major cause of drying out of foliage and soil causing possible major increases of water use. Further barriers to such wind should be contemplated.