They all tell me to got to Legal News because all mortgage related things are posted by them.

I am just worried this might be a mistake as it as a high cash flowing property and my mortgage rate is a low 3.125%.

As mentioned elsewhere, breakeven on cash flow is not the same as break even for taxes.Let's make some assumptions:Rental income = $1000Mortgage payment = $400 - but $300 is interest and $100 is principalOther expenses (repairs, advertising, utilities, etc) = $600Depreciation = $250The above scenario creates a break even from a cash flow perspective, however the tax scenario looks like this:Rental income minus the mortgage interest (principal is not deductible) minus the other expenses minus depreciation looks like this:1000-300-600-250 = $150 LossIf your income is over $150,000, then you cannot deduct that loss, but you can roll it over to future years. 

Here are my thoughts about your decision to refinance.Process:Understand your current loan terms.Check your credit score.Compare offers from different lenders.Get your property appraised.Submit your application and go through closing.Considerations:Current interest rates vs. your existing rate.Amount of equity built in one year.Closing costs and fees.Your long-term financial goals.It's a complex decision, so consulting a financial advisor or mortgage specialist might be helpful.

We’re looking at buying a rental and are trying to figure out the best course for taking a second mortgage out.

My realtor provided me with three names of folks he has worked with which is helpful.I spoke with the first one (who is a mortgage broker so not tied to one particular bank) and he said I would need to put 25% down on a vacation/2nd home, or at least 20%.

I am currently halfway through a gut rehab on a property which I completely own. I unfortunately self financed so my funds are tied up in this one house.  At this time in the project, is it possible to take out a loan...

All require the "lender" to be licensed in the state, for borrower to have no mortgage lates or hiccups, have different rules and change the rules whenever their investors (not government MBS these are big guns investment firms with pulse of the location where your property sits) see clouds in the sky.

They can’t delete your “old mortgage”.

[1] How are retirees living on rental income supposed to pay their mortgages?