Is it legal to publish health informations and violations by a business (public records released by the city) on a blog/site?

As long as you are telling the truth, no action against you for defamation would succeed.

You can't get a driver's license in Washington while your license is suspended in another State.

Can I protect myself and legal users from underage users on my NSFW Role Play hookup site?

See https://app.leg.wa.gov/RCW/default.aspx?cite=9.68A.040

Does my employer have to pay my 3 months of unused vacation time when I leave?

See http://www.lni.wa.gov/workplacerights/

Do I have any rights to information from my psychiatric counseling office?

You do have a right to ask to see and get a copy of your health...

Medical Bills that were covered by Insurance have come back after 14 years. There was nothing on the credit report?

Normally, there is a six year statute of limitations on written contracts. https://app.leg.wa.gov/RCW/default.aspx?cite=4.16.040

Friend let my brother borrow his car then reported it stolen . Reason why to avoid repo in Tacoma wa

Legally, if you are a witness to a crime, you should call the police.

Can I apply for driver license when my visa is expired?

You can apply, but there is no guarantee of acceptance.

What tickets are holding my license and how much will It cost to reinstate ?

See https://www.dol.wa.gov/licenseexpress.html You may have to pay your tickets.

What legal action can i take?

Perhaps you should write them a strongly worded letter setting forth the details and particulars of your complaint.