We know that non-attorneys cannot practice law or represent parties. But what about a wife or husband representing their spouse?

Representation of another person in a court of law is something only licensed attorneys can do in the State of Washington. In some cases,...

Will I be asked to pay a civil demand? And will I ever be able to shop at target?

See RCW 10.22. https://app.leg.wa.gov/RCW/default.aspx?cite=10.22

What matters is the preponderance of the evidence. See https://www.law.cornell.edu/uscode/text/10/934

What am I supposed to do? I paid $1100 plus tax for a phone. Company refuses to issue the refund.

You can complain to the AG. http://www.atg.wa.gov/file-complaint

Will I be able to work with teens and young adults with a finding of neglect from CPS?

Surely there is more to the story leading up to a "neglect finding". https://www.dcyf.wa.gov/services/child-welfare-system/cps

I am PRO SE in Washington State, and need to do a deposition of opposing party. Am I allowed to ask the questions>

You can usually ask the questions in a deposition when you are representing yourself. The existence of a restraining order complicates things. ...

Can I appeal any order on my custody case? Will that get me a different judge and a higher court room?

See the Rules of Appellate Procedure. http://www.courts.wa.gov/court_rules/?fa=court_rules.list&group=app&set=RAP

Complicated, verbal notice to vacate my shared home with recently deceased grandfather. What are my rights? Do I have any?

You should obtain a copy of the will and see what it says. Perhaps it is in a County Will Repository.

Can my employer withhold my paid training, for two months, from me?

Workers do have certain legal rights (i.e. minimum wage). See the L&I website. http://www.lni.wa.gov/workplacerights/

Can i sue a jeweller for selling me fake jewellery. Considering that he posed it off as real gold/diamond. I have the receipts.

There can be one or more causes of action at civil law for the circumstances your statement describes.