The glass door on the convection oven broke. Can I still use it

Assuming you do not have access to the instruction manual, and/or the manual does not specify whether it is safe to use the glass in convection/grill mode, I would assume not.

Are there any labels and/or writing embossed on the glass?

As I described in this similar question, "regular" soda-lime glass is not heat safe. Given that the glass was obviously designed for a microwave, it is probably tempered glass, so it can withstand some amount of heat. Therefore, I would treat it like a Pyrex baking dish and not heat it to over 500°F. Your microwave's convection mode likely does not get that hot, so you are probably fine with that, but no guarantees. I would not use the tray in grill mode because even Pyrex is not broiler-safe.

A convection oven has a fan that blows hot air around the items being baked. The air flow will draw moisture from the food. To stop the drying out, you could tent the baking items with aluminum foil but that has two drawbacks: you waste aluminum foil and lots of times you do want your baking items to lose moisture during baking. Another issue as you noticed, it messes up the browning (Maillard reaction) of the baking process. Where you place your item to be baked with a regular oven has a big effect as well as the container. The top of oven is hotter while the bottom of the oven is better for slow cooking. Place the dough in dark container for better browning. Convection ovens change all of those variables. I recommend that you use recipes tailored for that type of oven. If you are concerned about being energy efficient. Bake more than one thing at a time. That's what I do. I use multiple timers and the location in the oven to place the various items for a fantastic meal or bake.