No it will not cheak your tie rods .I'f it vibrate's when you press your brake's it's the rotors, fix it quick or the "vibrate" will keep losing lug nuts.
Yes.
yes
A car's steering wheel will vibrate when driving if the car's alignment needs to be adjusted.
If other things vibrate as well as the steering wheel you might have a damaged motor/transmission mount.
This is probably due to worn brake rotors on the brakes, if there is no vibration when driving then this will be the cause.
get a wheel alignment
Check your power steering fliud, if it is low this could cause the vibration you are feeling.
It is the engine that is vibrating and it is just being felt in the steering wheel. Can be a vacuum leak, or miss in the engine.
the motor mount is bad
Normally it is a tire out of balance. Can also be a bent wheel.
You possibly have warped brake rotors on the front. Or Bad Wheel Bearings.
Normally this is caused by a tire out of balance or a bent wheel.
could be a blockage in your fuel lines.