I have been a home owner for 8 years and I have always paid an additional ~10% of the monthly mortgage every month towards the principal of the loan.Any thoughts to whether or not this plan will help achieve financial independence sooner, or should I put this 10% into building a real estate fund?

Still building your portfolio: I would not pay down principal.

Remember every "no cost" refi you execute will still pad your principal balance. 

My question in the class was, how they define “investment” in the property, if they refer to just the mortgage principal, or if it includes any improvements done inside the unit. 

You could start a new company and find a broker, or someone easily licensed, like a NYS attorney, to partner with to be the principal broker for the organization.  

@Mathew Scott It really depends, nothing wrong with leverage as long as it makes sense numbers wise.If you like the numbers when principal pay down is factored in, than the deal may work for you.

I did find one bank that would refinance to a 15-year loan at a good rate, but that would involve throwing a lot of cash into principal to get the payment down to the point it keeps cashflowing strongly.I've only ever bought two places, this rental and the one I'm in now, but I had considered buying a 3rd place in DC before my next overseas stint. 

Focus on principal pay-down & leverage 1st.

They paid the bills but I didn't make much/anything other than paying down a bit of principal.

Pay the beneficiary the principal sum of $_______________________________ plus interest at____________________% per annum from _________________________, 20_____ to the date of closeof escrow;2.