Can I still drive my car of my registration expires this month?

Yes you "can" but if you do and are caught you will receive a citation.

Duh

Sure you can. Just don't get caught.

If you get caught, it's not the end of the world. It might be a huge and costly pain in the nuts, but it's still not the end of the world. Driving with an expired registration sticker isn't exactly the crime of the century, you know. You might not be towed and impounded (but you could be), you might not even be ticketed (but you could be), in fact you might just get off with a warning. It all depends on a) which cop stops you, b) how you interact with that cop and c) what kind of mood they're in.

When I got stopped with an expired tag, I just paid the fine and that was it. I was nice to the cop, so he 'forgot' to call a tow truck. I knew the risks, I gambled and lost, so I paid the penalty.

One thing is for sure if a cop stops you, they don't care who paid what in renewal fees. That stuff doesn't matter, the only thing that matters is whether or not you have proof of valid registration when you drive. Absolutely everyone says they paid the fees and are just waiting for the mail to arrive, so don't waste anyone's time with that excuse.

NOTE: You do know you can just pop into the DMV and get a temporary, right?

Not legally, no. You are legally obligated to display current registration on your vehicle at all times. Even though you have paid for your registration renewal any law enforcement officer could ticket you for failure to display current registration. Want to risk it? That's your call.

Yes, plenty of people do.

“Probably”. Did you print out the receipt for renewing your registration? If so, then keep a copy of it with you, in case you get stopped.

No, not without potentially getting a fine if you are pulled over.