First of all, good for you for getting out there and DO NOT worry about your time. There are days when just getting home in one piece is a triumph!

Second, you can put slicker tires on your bike. They do make slicker ones for bikes like yours. I don't know about how much you can change the width, though. I am still a newbie with that sort of thing!

Third, definitely drink and eat before a ride. Everyone is different. I love to eat a BIG meal before, but I don't want to eat a lot afterwards. If I will be riding for an hour or more, I bring a snack. If not, I probably won't.

Fourth, the weight question is one people ask a lot. I have lost weight, but gained a LOT more muscle while riding. You may not see weight loss and you may gain weight, after all as muscle weighs more. However, you will tone up and be healthier for doing so.