The current owner is passing me all the existing accounts for Hospitable, cameras, the alarm system, etc., though, so operationally, there shouldn't be any hiccups. 

She knew the camera was there.

What about adding a live-in nanny or au pair to the household who needs their own bedroom? 

I have installed surveillance camera in the front of my house and 3 days ago it captured that a pickup truck towed a coupe (a type of car) to the front of my house and the coupe has been since parked in front of my house.

Maybe consider some security cameras in the area to monitor activity outside?

Put in a camera. 

Do you guys use or suggest full security systems for your short term rentals or just use an external camera or two? 

Put it in the backyard under a tarp with a surveillance camera on it.

Does anyone know of any good home security systems with outside perimeter cameras that doesn't need wifi connections for a student rental?

So she decides to bring in a nanny/babysitter to care for her child and doesn't tell me that the babysitter will be bringing her own child with her to my rental to babysit both.