1. Ride on the street. The sidewalk is the side WALK, bicycles do not belong on it. Make sure you have good lights and you'll be fine on the road... after all, on a street that narrow you're probably going almost as fast as the cars are. I would say a helmet is a good backup but not as important as good lights and safe behavior. Your goal is to not get hit, because if you do get hit any protective gear will only help a limited amount. Use proper hand signals, ride in a predictable way (not weaving around), and obey all traffic signs. Be aware of your surroundings.

2. Stop at the stop lights! And stop signs! Yeah it's awkward. You know what else is awkward? Getting a ticket. Or getting run over. Try scooting forward so you're not on the seat anymore, that'll give you a couple more inches. If your bike is still too big for that, lower the seat or get a smaller bike as soon as you get the chance.

3. How big is your basket? I just swing my leg up over the milk crate behind my bike. Depending on your personal flexibility and comfort that may not work. You could try standing on a curb so you're a few inches higher, and/or tilting the bike towards you. If that doesn't work, try getting a set of "panniers" that sit down low on the sides of a rack. Or if you don't use it that much just take it off and carry stuff in a backpack!