I own my mobile home, but I rent the piece of land it sits on (not a mobile home lot but just a piece of property). I pay monthly rent to the landowner. I have some trees that are about to fall on my trailer. Am I responsible for cutting the trees, or is the landowner responsible?

Have you talked to the owner about this? Unfortunately, the answer to your question is that it depends. The first place I would look is to your lease, which may have some indication of who is responsible for trees, or at least for landscaping. At a minimum, it may specify exactly what land you’re renting (if the trees are outside the rented area, they’re almost certainly the owner’s responsibility).

Regardless of whose responsibility it is, the trees themselves probably belong to the owner, and should not be cut without the owner’s permission.