However, due to the leak, the water heater kept trying to heat water constantly and the electric bill doubled.

Electric, water, gas, sewer all have to be paid.

Year of update of the systems (roof, plumbing, electric, heat)4. any pets, pools, tranpolines, or business use at any locationThey will usually need more specifics but this is a good start. 

If you are covering the electric / fuel then one tank it is.

You do need to check electrical, plumbing, sewer, etc.

We haven't even covered if there is an issue in the other direction whereas, if there is property damage i.e. electrical fire becuase of the way the issue was approached, is the Tenant responsible?

Loosing deal for the bank, water, sewer, gas, electrical, lawn care, and trash added up to more that they collected. 

Agreed,Should have been removed during rehab process but sometimes it can be missed.Rehabbed hundreds and many times the crews miss stuff so not completely on the seller.I always tell our investors to have common sense when doing a building inspection.Anything that can affect the long term sustainability of the property like foundation, roof, mechanics, HWH, furnace, electrical, plumbing is on us.Any cosmetic stuff that won't really affect rent or cashflow is up to negotiation.If investor is adamant on being fixed, we will fix but at a cost.There is no such thing as perfection on 50-100 year old homes.The demographic in my area also doesn't require perfection.If they do, we don't rent to such folks and advise the suburbs which come at a 3x monthly rent compared to the city.The tree should be removed by the seller and foundation addressed.Doesn't look too major to me anyway.Thanks 

The gas is separate and the electric is combined, but I do split the electric bill between tenants.

Although they say they are paying gas and electric.