Neither party in the US can be said to support either of these if you look at the current state of affairs. Subsidies rig the market, and laws support cartel regulations in many industries that mean the idea that they are open to new entries is very far from the truth.
The large inheritance tax is at cross purposes to opposing monopolies, since you are taking away the family businesses and leaving public companies alone.
Why would a truly competitive market mean profits are close to zero?
Nah, it only fits a very theoretical model of what the US parties stand for in principle, or what they claim to stand for.
The second point would assume the existence of public companies outside of natural monopolies, where competition could not function anyway.
Regarding the third point they are presumably referring to this:
http://en.wikipedia.org/wiki/Perfect_competition#Profit