Noise from the left front wheel

SOURCE: I have a noise coming from the left side front

1) Take car to non dealer shops willing to give FREE opinion

2) Not likely you have a shock in Driver Front wheel, more likely a strut. Not likely strut needs to be replaced, but strut has a STRUT MOUNT (3 bolts of which can be seen when opening your hood) below this it is connected to STRUT BEARING which below it connects to UPPER SEAT OF STRUT or SPRING INSULATOR, that if loose will rattle. Usually, shops will not tighten, because to tighten is same labor as replace the parts. (Since you already dropped $1000 on ToyotaDealer, ask them to tighten FOR FREE since rattle is still there.)

3) There is a part called a "link," connects strut to stablizer bar, that if bushings are bad will rattle.
4) If stabilizer bar bushing(s) bad, will rattle early on but eventually clunking
5) Bad ball joint or tie rod can rattle as well

Never permit any shop to do expensive work on your car w/o first getting a second opinion somewhere else first. Do not tell second shop that you are there for a second opinion.

Shaking steering wheel at highway speed, no braking
1) Bad tire in front, bad tires in front, verify inflation of tires
2) Wheel alignment may be out
3) Front suspension parts (mentioned several above)

Highway speed to suddenly braking shakes steering wheel
1) Front brake rotors need to be inspected for warping
2) Test calipers on empty road at 40 mph, going straight on very LEVEL ROAD, hit brake pedal SOMEWHAT hard while barely touching steering wheel. If car jerks to one side, instead of braking straight on, you may have a caliper, ABS, or brake fluid pressure regulator off.
3) If brake rotors are warped, may as well replace front brake pads at same moment. Use ceramic.
4) When you drive on VERY LEVEL road on highway, steering wheel must be centered, let go lightly of steering wheel. Did car stay in middle of lane? No? Get a 4-wheel alignment.

SOURCE: vibration through car

If you don't have to be moving to get the vibration then it has to be either something is not balanced properly (torque converter may be bad, front pulley, engine flywheel cracked) or you have a bad mount, causing the vibration from making the engine or trans contact the car body in a place you can't see.
Hard to pinpoint without feeling it myself. I can say for sure it's not the cam belt, unless there's debris stuck to the inside of the cam gear causing the vibration.

SOURCE: I have a noise coming around my driver side front

SWAY LINKS OR INNER FENDER LOOSE

SOURCE: plastic panel came loose under car, near where front area close to underneath radiator?

just a guard to stop stones an general rubbish sticking to the bottom of the rad hope this helps

SOURCE: Toyota Corolla, manual 1991, Squeaking sound when turn the steeri

This is normal for a 210K Toyota Corolla. What you are hearing is the sound made by the power steering pump. Check fluid level and fill as needed. Some noise in the instances you are mentioning is normal.

Testimonial: "Thanks for the advice. When i checked the Power Steering fluid level I found that almost empty. Once i filled it up, it seems to be ok. thanks."