why I can't hire a new coach? i'm trying to hire a DC but it does not let me? only to free agent

You should be able to make an offer to any unemployed coach at any time, in what way is it not letting you? Possible reasons are that the coach is not unemployed, or if the coach is on your team - or on another team and you're in the early free agency stages where you can poach another team's coach - you are not offering a promotion, or the coach signed his current contract in the current season.

I can't offer a contract to a coach that is hired by a team. why? I'm trying to hire a DC so I want to promote a coach form another team to DC to my team

you can only offer a promotions to others team coach during the early stages of free agency. Other than that, you need to sign an unemployed coach only

so after the draft I can? there is another free agent stage

I believe that is too late to steal coaches from other teams. You can only do that during early free agency (before the draft). Once the draft starts, you are left to promote your own coaches or look to free agents.

thank you very much for the answers. I did not know that since I did not read about that any where.

Are the coaches salaries part of the cap number? If not, where do I find what is available to sign coaches?

No, it is a separate pool. You see what you have available when you offer a coach a contract.