What can I do with the situation?

Turn it over to your insurance or sue the at fault driver for your damages.

Can I sue the other drivers insurance for not totalling my car and my repair shop for not properly fixing it?

No you have no claim against the insurance company. You can demand that the repair shop adequately fix the vehicle.

What do I do when an insurance company won't settle on a law suit?

Not satisfied with the offer then take it to trial. However, you hired a lawyer for their advice. I suggest you listen to what they have to say....

The car behind is at fault for initiating the chain reaction

Possible to get it reduced or dismissed. Odds are better with legal representation.

They are never going to offer you more than you accepted. Talk to local counsel.

Possibly. You need to look into setting up a special needs trust to avoid the loss of any SSI benefits due tho the settlement.

What will happen if i have no insuraance and my registration is expired i was parked in the street and someone hit my car i kno?

Your lack of insurance has no relevancy to the damages sustained from thevat fault driver to your car. Move forward with no concerns.

Can I get compensation?

If he was at fault, you can sue for all damages sustained as a result of the negligence.

If is my situation considered a lawsuit?

The answer is in your lease. It will tell you what your and the landlord's responsibilities are regarding this issue.