Your story sounds to have a fair level of negligence, and depending on your contract, oh-yeah, there could be accountability there. 

The lender has no duty to the 2nd borrower and vice versa and in fact, the lender may be negligent to regulatory agencies, examiners, investors, the U.S.

How specific can you get in your lease when it comes to tenants responsibility for repairs of things to the house related to negligence, ie flushing sanitary products down toilets, appliances, hoa fines related to negligence of caring for the yard or following hoa rules etc? 

e.g. if we add a clause to the lease contract stating they will be liable for all charges due to their purposeful destruction or negligence, is this legally binding? 

If I decided to scrap the whole idea and just get a big umbrella policy with the exception of gross negligence are there really very many situations where the umbrella policy wouldn't hold up?

The laptop was not insured by you and (depending on local laws) without negligence on your part (ex. pipes were properly maintained by you, but one randomly burst), your insurance company is not going to pay to fix it.

If I had not done this and then let the tree fall on my home, then I could sue for negligence on their part but I'm not that type of person.

If they were negligent in the performance of their duties, then they owe damages caused as a result.

This is something on the manager that you can address yourself, so if they're incompetent or negligent, you're basically stuck. 

I didn't have a specific clause in the lease about dog poop, but the lease did state that I would charge $100/hr for any maintenance that was due to tenant negligence.