Can I (do something)?

There are lots of different ways to ask for permission to do something:

Can I ___? May I ___? Would it be all right if I ___? Would you mind if I ___?

In the situation above, you don't need to be too polite. So "Can I ___?" is a good choice. Use "Can I ___?" when you want to do something that doesn't cause trouble for the other person. It's also good for asking questions of people that you're close to or on a similar social level with.

drop off (something)

To "drop off" something means to leave it in a place. But you only use it for things that you leave on purpose, not by accident. For example:

I need to swing by the office and drop off a few documents.

Could you drop this off for me at the post office?