Hi Derreck,
Congrats on jumping into the deep end!
I recently created an LLC that is owned by my revocable trust and transferred my rental property into the LLC. So, to answer your first question, it is allowed in NH. As far as the charging order protection, I'm not sure about that. I think you may need to consult with a lawyer.
I will say that the way my LLC was filed with the state, it didn't really give me the level of anonymity that I thought it would since I am still named as the the manager of the LLC which is public record. I suppose if you can list the trust as the member or the manager of the LLC, and your name is not associated with it (except in the the operating agreement which is not public record) then you might be able to remain anonymous. But I don't know if that is possible. Again, I think it might be worth it to get some legal advice.
Good luck and let me know if you get any more info on this. I'd be curious to know what you find out.
Thanks,
Lou