If you sell or transfer the property - that basis is re-evaluated at the time of the new sale  and would likely increase - making your taxes higher.  

A cost segregation study looks at a property you own to breakdown the various assets you purchased.The goal is to increase the depreciation expense by finding assets that have an asset life less than 27.5(residential) or 39 years(non-residential).Whether you should get a cost segregation study done is whether you will benefit from the study.Will you be able to use the added depreciation now or in the near future?

Appraisals have to be done at an "arms length" from the bank, meaning the bank can't influence the value.

We do want to offer flexibility, our goal is to keep the tenants so if increasing only $25 a month the first year keeps them we are open to it. 

.- Getting tenants to agree to rent increases and turning in all the required paperwork to caseworker, then, you guessed it, chasing them to process it- Dealing with the tenant's "entitlement attitude" that they don't have to follow the terms of the lease, so they move in other individuals and/or get pets without permission.So, a good PMC will charge something more to manage a S8 tenant/property - either a higher percentage or a one-time or annual fee.

After I rehab it let’s say I put $30K in rehab work, on average how much would my property increase in value?

Investing in distant markets increases your risk and/or increases your costs. 

Do you think values in 39212 (SouthJackson) have increased since 2018?

get quotes, run the numbers.on the addition - it's almost definitely not worth it, i suspect the time to pay the costs back for the increase in rent might be decades or longer. 

Increasing your construction budget by a small amount can have an enormous impact on your overall construction budget, productivity and site safety/insurance premiums.