Lending or licensing a patent to a 501c3

I hold an LLC and set up a 501c3 (separate entities). I am currently board chair for the 501c3. My questions are the following:

1) Preferred option: Can I as an individual or my LLC patent a new product and then license, lend or donate the product to the organization for development and use in a program? No money would be exchanged at any time because the product and "licensing" is intended to be free. If it is allowed, the other board members agree to this plan.

2) If not, can the 501c3 be the one to file a patent itself?

3) Can the LLC do the same as described above by lending physical assets, such as loaning (for free) software and tech equipment owned by the LLC?

4) Would it help if I refrained from writing off the value of the donations on my LLC taxes so as to minimize any perception of self-dealing?

Edit: Added question

Thanks!

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