Would My fiancée have good case against a man who sold him an unsmog and failed smog car in small claims?

In California, the seller is responsible for smogging the car.

Is it acceptable/legal to cancel the Installation Proposal and date of installation via email or fax?

It sounds reasonable. Follow up with a phone call to verify that they received it.

I owe EDD and i received the Judgment yesterday, would EDD take my federal and stated tax refund?

Yes. Cross your fingers. Good luck!

Is a unlawful detainer action consider to be a breach of contract under 1812.10?

Probably not. What are you getting at? You need to look at the Unlawful Detainer statute. A lease is not a good or service.

Am i obligated to pay a $250 contract modification fee. If an Auto dealer with inhouse financing gave me false ssn information?

I hope your father didn't cosign. This dealer is too shady to let him off the contract if he did sign it. Take the car back and rescind the...

My pitbull got out the yard am I liable?

Usually, yes, you are liable. See other answer for possible options.

Can you cancel a signed Installation Proposal to install a new HVAC in Arizona?

You now have the choice of going through with the proposal/contract, or asking them to cancel the installation date. Don't wait too long.

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Dog ownership- the dogs' registration/county tags is in her name is that person the legal owner?

That is one of the prime indicia of ownership.

Who pays for any outstanding loans/liens on a bequeathed title and interest of a vehicle?

The heir would be responsible for outstanding loans, unless they refuse the gift.

Residency

No, you can stay in the home, even if he is there.