In this industry reputation is very important.  4.

Is there a way to know if an online real estate license course is reputable/accredited/accepted? 

What you think you'll save, you will spend in purchasing.Find an honest, reputable builder that will work hand and hand with you and in the end, you'll be a happy man.Luke 14:28  For which of you, desiring to build a tower, does not first sit down and count the cost, whether he has enough to complete it?

But I've been dealing with a reputable real estate agent that is telling me that a cap rate of 5% is not unreasonable...

Start immediately with the 8% who might not have the best service reputation but they're in your affordability range.Whatever you do, be honest with your expectations. 

The biggest turnkey company of repute only works in two or three markets.

Find a reputable lender that can tell you what they offer in your area!

then use your remaining 100k cash reserves and invest with a reputable apartment syndication company such as davidenko or myself so you can cashflow 10% preferred for 2 years while you househack learn and utilize homestead law etc.

What is a good way to find a reputable, experienced company that rehabs apartment complexes?

I would recommend finding a reputable local operator if you're not looking to join a program.