let me try to explain it in a few words: margin is the amount of money required to open a trade. Free margin is the amount of money in your account available to open new trades based on your current margin use and equity. So Equity-Margin= free margin. The free margin available will increase/decrease depending on the profit (or loss) of your open position. I hope it makes sense. sorry I forgot to mention the equity, yes you are correct, equity is your current account value if you were to close all trades at that time.
A stock or any other security representing an ownership interest. In terms of investment strategies, equity (stocks) is one of the principal asset classes. The other two are fixed-income (bonds) and cash/cash-equivalents. These are used in asset allocation planning to structure a desired risk and return profile for an investor's portfolio.