Or should I hard money loan this and not worry about that period?

The best opportunity you will have to replacing out-dated systems (plumbing, electrical, HVAC) and improve the energy efficiency of the building envelope (air sealing, insulation, fenestration) is before a building is placed into service.  

Do you shy away from those deals or would you take them on and hold them for a period until the cash flow surpasses the difference between the current cap rate and the historical cap rate?

My long term goal is to buy and hold (and hopefully through BRRRR strategy - as I see it as a very efficient way to build equity and portfolio).

Our property manager since she manages hundreds of units, her whole team has to stay very organized to make sure that units are being managed in an efficient manner! 

I don't usually do that but there was a flood that caved in a garage foundation wall during the due diligence period so definitely made sense under the circumstances. 

I do like my PM company as they are professional and efficient and all these fixes sound necessary to me.

You could always try it at the 90 day seasoning period.

Is your tool going to be able to physically call the assessor to find out what taxes are owed and how is your tool going to account for the timing adjustments of billing periods for taxes?

PERIOD.