First, the building issue. There is no problem with both of the charities operating out of the same building. There is no conflict of interest here. However, on behalf of the Ministry, which owns the building, in order for you to properly account to the Ministry and be fair, each charity should pay some rent to the Ministry.
Second, the conflict of interest. You can hire or fire people for the nonprofit that also work for the school, that is no problem. As long as they have the proper qualifications for the job, and you are hiring them at a fair market rate (not inflated) for what the job is worth, you are fine.
Third, your charity does not have to be restricted to religious purposes. Have you already received your 501c3 status from the IRS for the charities? If so, what did you specify as the purposes on the 1023 application? Or is the charity also going to operate under the ministry's 501c3 status. If so, you may be restricted to religious purposes - that depends upon the terms of the ministry's allowing you to use their charitable umbrella.
The most important thing in your situation will be entity separation. It will be very important to run each entity - the two charities and the ministry - completely separately. Keep separate books, bank accounts, staff, etc. for each. Make sure they operate at arms length with each other (paying one another for rent, services, etc.). As long as you do that, you won't have any problems with conflict of interest.