I am a planner type of person and am trying to build my own guide for home buying. 

One of the stipulations for the sale was to provide effort to remove 2 problem tenants in the building.

(Hey may be buying new builds with lots of closing dates available, or they may have negotiated flexible closing on the property they ar buying.).

I'm just beginning my journey in real estate with a goal to flip properties and build a portfolio of rental properties.

You can look at the after repair value and subtract your costs. for example if it is worth $2M after fixing up, costs $1.5M to build, then the land is worth $500K.2.

New investor here looking to build my network out with property managers in the area.

This additional liquidity could be used to improve their credit score and build savings, enhancing the likelihood of a successful refinance.3.

Or does it purely my choice of whether I want cash flow or equity build? 

I got the owners to agree to pay for a new water heater for the building (about $4000), and $10,000 of seller paid closing costs.

If the price to replace is within budget I'd do it because you're putting out a newer/safer/more reliable product.2) Cost to replace the entire systems is tough to gauge without knowing the building size and style...