Direct democracy: Every man's vote is directly counted, and the majority's decision is absolute and rights of the majority are not respected. Example: Town Hall meeting with a show of hands for a vote on a law.
Indirect democracy: Citizens vote for representatives. These representative's decisions are absolute, and rights of the majority are not respected. Example: Current US Government.
It's really not all that complicated.
rights of the majority are not respected
Should be "rights of the minority are not respected."
Even if that were a precise definition of so-called indirect democracy (and it's not) it doesn't describe the USA at all. My representative's decisions are absolute? Really? Rep. Scott Garrett from NJ has absolute power? I better call him and let him know. I wonder how he will handle it when he finds out Sens. Lautenberg and Corzine also have absolute power. And since their decisions are absolute, I'd better shoot off an email to the SCOTUS and tell them they are no longer needed. And same goes for the President. I'd better tell him his veto is not going to be needed (although with this President, why bother?)
You see how your descriptions don't match reality? By the way, if you look up the meaning of "republic" circa the time of the Founders, you know what it means? It means a) no monarch, b) the people "own" the government and c) representation by elected officials. In other words, to the founders, representative democracy, which they called republicanism, so as to be more precise. When they spoke of democracy, they meant direct democracy, which we clearly don't have. (Although some states do.)