Can a swab paternity be wrong?

DNA tests are usually considered very accurate. Perhaps you should have it re-done.

Will I have any tax concerns if I elect to have dual US/Luxembourg citizenship, but only live and work in the US?

You should probably ask a lawyer in Luxemburg. The U.S. IRS expects all U.S. citizens to pay taxes on all income, from whatever source received.

Land Inheritance

The IRS expects you to pay taxes on all income, from whatever source received. Washington State also taxes real estate transactions...

When your work company is going to take money out of your check, shouldn't they notify you ?

The L&I website has some good information about workplace rights. http://www.lni.wa.gov/workplacerights/

Why is adult protective services still investigating?

See https://www.dshs.wa.gov/altsa/home-and-community-services/adult-abuse-and-prevention

What should I do? Can I do something about it

The L&I website has some good information about workplace rights. http://www.lni.wa.gov/workplacerights/

Sole Proprietor or LLC?

The main advantage of a LLC is the potential to protect your personal assets apart from your business assets. Where you are, in fact, the sole...

My STEM extension got rejected as I did not sign on I-765 form in applicants signature column so should I need to pay the fee to

There probably isn't any practical way to challenge that kind of decision by the USCIS.

It can I get money back for all the test they should not have done.

Try to negotiate a settlement agreement with the vet.

See RCW 9A.86.010 https://app.leg.wa.gov/RCW/default.aspx?cite=9A.86.010