I have a few Yale Assure 2's, and the battery life is $hit.

Batteries should last a while in warm weather.

Given AirBnB is all rating and reviews, I do not want the risk of someones phone being dead, the internet being down, or batteries being dead, etc.  

TASK Confirm all dwellings equipped with the proper security devices Replace all batteries in smoke and carbon dioxide detectors once a year.

Just cross out the parts of the new lease you don't agree with and sign and initial and date next to it.Have all tenants over 18 sign just like you did.In fact I would print name,sign name,initial and date for each area crossed out if you want to be ultra cautious.The landlord will have to agree,come back with a compromise,or get you out.They will have lost rent and reconditioning cost.So if you pay on time most likely they will not want to lose you over this.The fact that they overpaid for the house and are having a hard time covering the mortgage is NOT your problem as a tenant.You didn't hold their hand to the papers they signed at closing.Sounds like they put a bad tenant in and they trashed the place.You came along and the landlord barely had money to fix things.So see if they will keep the regular lease in place and don't get onto them too bad for too many more repairs.It sounds like they are headed to foreclosure or close to it as it is.no legal advice

I had to bring my car battery home with me at night lest it be stolen.  

I would recommend bringing some extra batteries in case one of the smoke detectors dies before he shows up. 

A concern would be that the batteries would be dead forcing my tenants to be locked out. 

Other than that, soap, some batteries AA & AAA & 9v, notepad pen dishwasher tabs a smelly candle dog treats poop bags TP paper towel a colouring book/ crayons if they have a kid some Lysol wipes and such. $20 gift certificate for pizza joint hand written “moving sucks, this may help”.

Get the smoke detectors with 10 year batteries, put one in every bedroom, every hallway, and everywhere but the kitchen.