RE: the double-taxed income form (worked remotely from one state, paid all taxes in work state ) There's two columns, the work state "amount" and my "amount." How 2 fill?

Your amount is the amount of double-taxed income in your column. 

The work state amount is the amount being taxed by your work state. Your amount is the amount of work state income tax being double-taxed.

These amounts are usually the same. However, there can be differences. For example, some states don’t tax unemployment benefits. If your work state taxed unemployment, but unemployment was not taxed in your home state, you would enter $10,000, for example, in the work state and $0 in your state.