In general, if you borrow money to buy investments, that interest is deductible against your investment income on form 4952. There are special rules when you borrow against your home. Briefly, you have two choices:
A. Consider the interest as a mortgage secured by the home. In that case, it is only deductible on schedule A, subject to the usual limits on mortgage interest deductions (including the $750,000 cap and the rule about acquisition debt).
B. Consider the interest as "not secured" by your home. In that case, you can consider it to be interest used to purchase investments which is deductible against investment income on form 4952. However, by declaring the interest as "not secured" by the home, you give up forever the ability to consider it a deductible mortgage on schedule A, even if you later change your mind.
Also, for any loan you take to buy investments, the interest must be traceable to the investment. For example, if you take out and HELOC and use some of the proceeds to buy an investment and some to take a vacation or remodel your home, it becomes difficult to trace each dollar of interest to either the investment or the other personal purposes.
I can't comment on how much trading you must do to qualify to file on schedule C. I know it's possible, but uncommon.
