The rental is pretty old and the plumbing in the basement is starting to show blue corrosion on the pipes and I am concerned this will lead to bigger issues in the future.I don't feel comfortable taking on this as a DIY as I believe there will need to be soldering done to remove/replace some sections.

Corrosion will happen regardless of whether it's gas or electric, so it's worth doing it for both.Also, my understanding is that since the gas heater's burners are at the bottom, the sediment can act as an insulator, reducing efficiency (although there are varying opinions on this.)Prior to flushing the tank, you should test the TPR valve.

Regarding the screen, recommend any types that are corrosion resistant? 

Old metal lines are usually so packed with corrosion that your water barley flows.I probably would not purchase as a rental but definatly as a flip assuming price adjustment to reflect costs.

@Babatunde Onadele JrI would guess the winters and the amount of snow would have an impact.The lake is not salt water so you do not have the corrosion you have near oceans

But did they detect corrosion and damage in cases like this?

The plastic handles would strip from the shutoff cylinders as the corrosion was excessive & the water dripped constantly, those high water bills would eventually pay for a new bathroom.

Ovens are enclosed so exempt.3 - All plugs and switches must be replaced with certified aluminum ratedOR needs a non corrosive grease (available at any Home Depot, Lowe's, etc.) on ALL plugs, switches, light connectors.

A few things came up though1)  Front Porch was separating (not the foundation)2)  Rear Left Gutter/down spout disconnected3)  Hot Water tanks connections have corrosion (they're replacing the whole unit)4)  Rear back deck is missing a "board"5)  Inside the crawl space, evidence of water intrusion6)  Inside the crawl space, under Master Bath a PVC has a slow leakThe seller is covering everything above. 

I don't have the tools or parts or talent to take apart the faucet, which usually has hard water corrosion and replace the washers.