Usually on a new car the problem is incorrectly torqued wheels. Your owners manual will tell you how to do this. If not, loosen all wheel nuts on one wheel at a time. Then retighten each nut in an X patern.
check brake rotors.
The steering wheel shimmering could be warped front rotors, when slowing down. The stalling when slowing down could be a bad fuel filter.
If you feel any vibration or shimmy in the steering wheel or if you feel the same things in the vehicle you have a tire out of balance. As you need to rotate your tires at least every 10,000 miles that is a good time to have the tire balance checked.
Check the tires for cupping. If you have had an alignment problem the tires could be cupping and will make quite a lot of noise. It could also be a wheel bearing.
Check the suspension and steering assembly for loose/worn parts, such as ball joints, tie rod ends, idler arm, pitman arm, steering stabilizer (if equipped), steering box, wheel bearings, shock absorbers, wheel balance, tires and wheels. Replace any bad parts and have the front end aligned.
probably a wheel bearing, ball joint, tie rod end, or tire balance issue. A bad CV joint is possible but unlikely. a severely bent rim will also cause a shimmy but usually at a higher speed.
Check your brakes every 6 months to see what type of wear and tear is happening. Of course if you hear a metal grinding or feel a shimmy in the front end have them checked at that time. Newer cars have sensors that indicate when brakes are bad. I usually have my brakes checked when I have my tires changed, about once a year. Depending on the amount of driving you do this could vary. Brakes have a 'squeal' factor to them, also. If you hear a high pitched squeal when you step on the brakes, it is an indicator that they should be checked and probably replaced. Dealerships check the brakes at the same time they do tuneups. Next time you take the car in, ask for a list of the items they check at the tune up times. Most check every 15,000 miles, or about once a year.
Tires/wheels out of balance?
1,000 miles
maybe the power steering fluid is low or your timing belt could be going
It depends on the kind of brake pad you buy, but it goes by miles. Some brakes need to be replaced after you have put 10,000 miles on them and some don't need to be changed until 60,000 miles.
To properly bed in new brakes for optimal performance, follow these steps: Start by driving at a moderate speed and applying the brakes gently to gradually increase the temperature of the brake pads and rotors. After a few stops, increase the braking force slightly to further heat up the brakes. Repeat this process of gradually increasing brake pressure and allowing the brakes to cool down between stops. Avoid coming to a complete stop during the bedding-in process to prevent uneven pad deposits. Continue this process for about 300-500 miles to ensure the brakes are properly bedded in for optimal performance.