Can you take a sip from your water bottle without veering into traffic?
What works for me is to be sure to maintain my balance and remain centered over the bike. I just angle my head back and sideways. This allows me to still see ahead, drink my water, and maintain my line.

Can you bunny hop over a pot hole instead of swerving?
If you can't bunny hop you should learn. It really is a safety issue when you have the option to just sail over debris instead of chosing to either hit it or veer into traffic. Crouch down pushing your weight into your feet, then spring upwards evenly with your hands and feet and your bike will lift off the ground. Don't forget to maintain your speed to ensure you miss your hazard.

Can you turn your head and maintain your line?
The key is to turn your head and rest your chin on your shoulder. Don't try to turn your whole body.

What other bike handling skills do you have/recommend
Ride rollers to generally improve your handling skills. MTB if you can as well.