Welcome to cycling and to the board!

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Here are some rambling thoughts:
How long/many times a week?
I'd try about 3 times per week for 30 minutes to start with. Ride at a comfortable pace until your body gets familiar with the new exercise. As you get into better shape, you can increase the duration, frequency, and intensity. Don't always ride at full speed. Slower rides can help your body recover.
Necessary precautions? Helmet? Riding against traffic, etc..?
I think a helmet is an absolute must. I've heard too many stories of riders sustaining serious head injuries due to not wearing a helmet. Always wear bright clothing when riding. Use lights and reflectors at night. Always ride with traffic, and obey all the road rules just like if you were in a car. Beware of riding close to parked cars. If a door opens quickly, it will ruin your day. When approaching a car at an intersection make sure that you make eye contact before putting yourself in their way. Many motorists won't see you.
Getting a quality bike that fits you well makes a huge difference. In almost all cases, though, be prepared for some pain in the seat when you first start riding. This gets better with time, but I find the seats with cutouts in the center are much more comfortable from the beginning. Initially, the seat should be level with the ground. If you are experiencing pain, try adjusting the angle up and down and back and forth in small increments. This can make a big diference. Padded cycling shorts also are very helpful as long as they are of
high quality.
What body parts will I tone by eating right and cycling?
Cycling does a good job strengthening the quads, hamstrings, and calves. It also helps develop the muscles on the front side of your lower leg. These muscles are hard to exercise in the gym. Unless you do a lot of hard sprint training, this will be predominantly endurance strength and not size.
How long does it take to see results?
It depends on where you start from. You should be able to increase both duration and intensity at a pretty steady pace; as you do so, you will notice your cardiovascular fitness also improving. If you ride 3 times per week, you will make great progress in a couple of months.