Consumer law. If the company who wrote the contract arbitrarily breaks the contract, am I still bound by arbitration clause?

The first step in interpreting a contract is to read it.

Can an ex law enforcement records and warrant searches clerk legally run my plates?

See the Vehicle Records Request Instructions from the...

How do you get cooperation from a district court clerk when the clerk is sitting on the notice of appeal.

See http://www.courts.wa.gov/court_rules/?fa=court_rules.display&group=clj&set=RALJ&ruleid=cljralj02.4 (There is a filing fee.)

My city won't remove and dispose of a 55 gallon barrel of hazardous waste abandoned 2 feet from my property.

Maybe you should call the police.

Yes yes I'm looking to find out if there's any open cases against me?

You can search court cases online: http://www.courts.wa.gov/

How do I clear my name from someone slandering me?

Technically, you may have a cause of action for defamation of character, but as a practical matter it appears unlikely you would get enough money...

You can make a claim with your own insurance company if you had available coverage. You can demand payment from the at fault party. You can sue. ...

Can i sued libel case if i sing a song and did not mentioned any name?

It appears unlikely that your circumstances comprise a cause of action at civil law.

The police can arrest you after you committed a crime.

What do I need to do to be compliant?

See the Pierce County Local Rules: https://www.co.pierce.wa.us/DocumentCenter/View/3148/Local-Court-Rules?bidId= The Confirmation of Joinder...