State tax filing

I hope I can follow up with my own similar question here:

 

I will be working a permanent remote position for a company in WA while residing in OH.  Since WA does not have individual tax income, I wouldn't have to file nonresident income tax for WA or deal with tax credit from WA correct? I would only file individual income tax for OH?

 

Do tax deductions work the same as Self-Employment taxes if equipment and office space is not provided/paid for by the company or is that dealt with differently?

 

Would I need to pay estimated taxes as a remote employee (not self-employed contractor/freelancer)?

 

How does this work on the employers end: Would they only need to file a W-2 with my residing address?

 

Would my employer be required to do tax withholdings and what "set up" is needed?