Is my car considered a lemon

No lemon law coverage for used cars.

Private sale of auto in Washington State. Is the car considered sold "as Is"?

"as is" only applies to sales by merchants in that type of goods. Private parties are not merchants.

What legal rights do i have if I bought car at buy here pay here lot and in less than 1 week I can count 4-5 things that broke?

"Revocation of acceptance" and "cancellation of the contract" under your version of the UCC. You will need a lawyer, though.

What do I do in order to return a vehicle that I purchased where financing was not approved?

This is bullshit. Violation of TILA and ECOA, probably. Find a qualified lawyer in TX (email if you can't) and sue.

I bought a car from dealership in VA on Feb. Now they are telling me today they need car back bank didnt finance

Violation of TILA and ECOA. Find a qualified PA lawyer (email me if you can't) and sue. There is some $$$ in this case, esp. if they do not...

Get a qualified attorney in TX (email me if you can't find one) and sue. This is fraud.

Can i sue a car dealer for forging our signatures and initials and not complying with amount agreed upon?

The answer is very simple. You should find a qualified lawyer (email me if you can't) and sue.

What can I do about this?

You obviously need to undo the transaction. "Revocation of acceptance" and "cancellation of the contract." You will need a lawyer for that.

Only if you get caught! Tsk tsk tsk. People in California . . .

Can i be sued in two different cities for the same case

You will need a lawyer to address these multiple lawsuits.