Yes they are supposed have endless hot water but they can only heat it so fast and a smaller unit will not keep up with a shower and the clothes or dish washer.One of the biggest problems for tankless water heaters is improper installation especially for natural gas versions.

Don't tell my landlord.As long as they aren't pumping water into your pipes with pressure, then it's just the same thing as washing a lot of dishes or taking a shower - if the washer is just draining instead of forcing water with pressure.If they're paying the utility bills, including electricity and water (and gas if the dryer is gas), then I'd let them.The only other thing I can think of would be humidity. 

After they were gone, and the place cleaned out, took 3 months, roaches totally disappeared, the rental unit and adjoining units.The chief reason we found with these tenants is they leave dirty dishes in the sink, don't wipe off tables after they eat etc.

Dawn dish soap works wonders with some elbow grease.

There was not enough for dishes...I finally replaced the 15 year old water heater myself and didn't renew the policy.FWIW, , I was told by that code enforcement officer that American Home Shield gave him problems, as well as other people he knew, and apparently are/were the defendants in (various) lawsuits.

All of my houses have had dish washers.

--Washing dishes:  Use a coffeemaker (for hot water) and fillable dishwashing wand. 

Just kidding but having mice in the house is unsettling and gross, especially if they are getting into your food and dishes.  

It would take a LOT of candles to do that though.Mild dish soap and water should remove it.

Nothing major - a fun-colored pot, dish towels, a bowl of colorful fruit and flowers in the kitchen; a shower curtain and towels in the bathroom; etc.