If I were you I would want to wait, 3-6 months to refinance my primary, as its a given that the interest rates will be lower in 6 months.Depending on your interest rates from your 1st mortgage and 2nd heloc, you can turn your Heloc into an amortizing loan by making payments on it every month. 

I wanted to fill the 'educational' void after studying intensely for months to pass these exams.

This sounds like an excellent candidate for a "wrap" or all inclusive deed of trust where you would pay the seller and lender (through a title company or loan servicing company) the new, agreed upon payment based on what terms you negotiate. 

-400/month.

The lender was adamant the City of Philadelphia could sell the property in a tax sale before their loan came due in 5 months.

I was told by the realtor that 750-800 per bedroom per month is the prior and expected rent.

Fast forward 90 days later and I have closed on two properties and I have another one under contract to close before the end of the month. 

This lead me to finding the bigger pockets podcast on YouTube a few months ago, and then eventually to the real estate rookie podcast.

While I know I can start a business making around $7k a month, my immediate goal is to house hack, and my concern is about qualifying for an FHA loan.Any insights you have on this would be greatly appreciated!

Make sure that the new property can pay its own mortgage and the HELOC monthly payments when doing the underwriting on the new property.