However, if the market is hot and you are not in a position to develop you may have given the deal to the developer.  

Lastly what would the typical % of profit split be in a 50/50 investor equity split on a flip?

Then once you figure out how much you have to put down, determine if it makes sense to shop a deal for an equity partner, or seek private lending/HML to fund the deal.

I work a full-time job but would like to spend the next 5-10 years studying hard and learning more to put myself in a position where I can invest wisely (and be diversified, of course) in real estate.  

They usually come with built in equity even after repairs.  

I am self-employed and take out large deductions, so using returns for income verification is a problem.Do I have any options to pull out equity from these properties, or do I have to turn to hard money to fund this flip?

Many times people in these situations do not want to sell, so when a buyer gets a person ready to sell it is a motivated seller.In these situations the person in any of those situation mentioned above may have more debt on the house than what the value of the home is, or the value of the home after rehab and purchase still will not give the investor as much return on their money that would make sense since there is not enough equity.

They often put in sweat equity as a portion of their option consideration.  

Applying for a HELOC: with 20% equity in the residence and considering taking out a line of credit to fund a down payment for an investment property in Chicago, Austin, or Pittsburgh.  

My newest purchase and my personal residence are 100% equity.