To Ride or Drive...
Depends on what you want. The bike is fun but the kid won't be able to ride on it for years. If you want to spend time and enjoy a hobby with the kid and mom then get the car done. I've been wanting another bike but at this point my oil girl is only 3 years old. Not gonna leave her and mom home when I want to go places so the bike will wait and I will work on the cars.
As far as marriage goes. No need man. Don't let anyone pressure you into it. A stupid piece of paper isn't going to make a difference in your commitment or loyalty to your girlfriend. The biggest thing is to treat the baby and mom right.