If I'm in the 2nd week of early free agency and have a few coaches I feel are making way too much (crappy position coaches) does their salary still count for the current season if I hire a much cheaper option?

No, the coaches salaries dont work the same way as a players does, if you replace a coach that has say a 1.5 million contract with another at .5 mil toy will save that 1 mil. The amount you can spend I believe has something to do with the teams attendance.

If you promote a coach up to DC/OC/HC that coach you replaced will go into the market the next day and other teams will be able to bid for his services