how can I attach screws perpendicularly to an aluminum sheet
When you say "simple drill" is this an electric drill or hand-powered? If it's electric you should be able to drill into it with a decent drill bit. You can *generally use woodworking tools (saws, drills, files, etc) on aluminum, unless you have some sort of exotic hardened aluminum.

You can use epoxy to join aluminum. Make sure both surfaces are clean and dry. A little scuffing with sandpaper would help it get a better grip.

This is dependent on the use for the item, also. If it is not highly stressed,  you should be fine.

*generally, as in not EVERY single wood working tool.