Can a private business deduct from their taxes donated rental space? If they lease their space out during non-business hours, what is the standard deduction?

Yes according to me the donated things can be deducted from the tax.

Yes, they can deduct the fmv of the leased space.

It depends; according to the IRS, office space donations are called "in-kind donations". The IRS encourages in-kind donations by allowing biz to take a tax deduction for the FMV of the service. For office space, this is the FMV of a lease. To qualify for tax dedcution, the recipient must be a tax-exempt charitable organization or 501(c)(3). IRS rules DO NOT ALLOW donations for a portion of the owner's interest in a property. For example, if you own a multi-story building and allow a nonprofit to occupy one of the floors for free, you cannot take a deduction. The reasoning is that because you still own the building, you have lost no benefit of ownership.