They moved to a new house in a better township and brought my siblings with them and my growing family gets to move into my childhood home.  

if it's an inheritance, I'd assume your siblings also inherited or I'd give them $10k each. 

Homeless for 4 months with my mother & siblings, they wouldn't let me go to high school because we had no permanent address.

She cannot invest the IRA herself or invest with anyone in the direct line of her family tree, ie you, or your siblings, etc.

What if I allow the individual that says they are the executor into the unit, they take some of the belongings, and suddenly another family member contacts me letting me know that I allowed a sibling, for example, to take belongings that technically belong to the estate and that they weren't the executor.

Are there other siblings that would see this as distribution of the estate?

I know she is not the only sibling and to my knowledge, the daughter didn’t live there before her passing (but I don’t know for sure).Anyway, the only person in the lease is The Mother.  

Currently my father owns a property that he is looking to give to my sibling and I (used as a rental).

My title company is now trying to track down all his siblings to sign affidavits to clear any claims on the property.

Yeah...that's not going to work...and will likely make the situation worse.If your parents want to keep the property and keep things amiable, they should offer to buy him out (or some combination of your parents, you and/or your siblings should offer to buy him out) at FMV.