I might advise increasing that to $500K or $1 Million as the cost difference should be negligible and if you do have a liability claim where someone is injured, the costs can escalate pretty quickly depending upon the severity of the injury. 

My second question is if I hire a traditional builder or developer to build on the lot which I own, am I better of from a liability standpoint to then deed the lot over to the builder (presumably so its on them if a worker is injured) and then have the property deeded back to me when done?

-Liability: If they get injured improving your property, and they aren't licensed, bonded and insure, their kids might come after you for injuries!

Someone living there 50% of the time means more wear on the apartment.6) The more people who live somewhere, the more people that could get injured and the more liability that there could be.7) Maybe he just wants all adults who live there 50% of the time or more to be background checked or something.8) Or, perhaps it's still #1 -- he's bored, nosy, or wants more rent.Maybe your landlord is worried that this girl will try to claim occupancy or stay there after you leave.

most investors do not know this, but if you hire a company to do work at your job site, and someone is injured and does not have work comp insurance, YOU are responsible for their injuries.  

What if someone gets injured on your jobsite?  

I'd be drawing a hard line with these tenants, with an official company letter notifying them of their breaking the lease terms by operating space heaters in your property, I'd also be pursuing having them pay for the electrical problems you're paying for or at least notifying them that you're examining the issue and will be deciding whether they are liable for the damages.Next time, next winter, or next month you could be instead answering the phone from the fire dept that your property burned down or the police that a tenant died or were injured in a house fire caused by space heaters that they have used because the landlord never said the couldn't, no record exists of you denying their use and then the next call is from someone's attorney suing you for a wrongful death, based on the precedent that at one time they had to use them because you admitted or inferred that there was a heating issue with the property due to them contacting you about an excessively high heating bill and at that time you were pursuing all sorts of corrections to the problem.Instead I'd be telling the tenants there is nothing wrong with the place, stop opening the windows and space heaters aren't allowed.I can't tell you the amount of tenants who have tried to tell me what was wrong with something based on a symptom.

MIL got injured and can no longer babysit my 9 month old.

If you have an inviting path and dock on a pound it won't be long until kids are there and sence it's private property expect to deal with the parents of an injured or drowned child.

Should I have the independent workers sign a waiver to limit my liability if one of them gets injured?