Does the US system reflect the principle of political equality?
Political Equality: the principle which means that each person carries equal weight in voting and other forms of political decision-making.
[I have edited your question because we are not supposed to answer more than one question at a time.]
First of all, I'd argue a bit with your definition of political equality. I do not think that every person has to have equal weight in political decision making. They just have to have the chance to have equal weight. In other words, I have much less say in the country's affairs than Harry Reid does, but I could conceivably become a Senator if I wanted to.
I think that we do have political equality, but it is not perfect. We do all have the right to vote and our votes count more or less equally. In that sense, we do have political equality.
However, you can argue that we do not have complete political equality because of the extent to which money talks in our system. A person with a lot of money can buy access to political decision makers and can pay for ads proclaiming their point of view. These people, then, have more potential power than I would have no matter how much I wanted to influence the system.
In regards to popular sovereignty: Even at the time of the founding of this country, people with money and influence always had more of a say in how things would work than folks without one or the other or both. This isn't anything new, and though some decry the current state of affairs, it isn't a massive change from previous conditions. And compared to other countries, the ability of the voters to make their voice heard is still pretty darn good.
As far as political equality is concerned, the previous answer goes for this one to a large extent as well. People without power can at times make a difference, but massive amounts of wealth and the ear of the right people can often make more immediate and significant impacts.
In terms of free speech, I would consider this to be our most powerful example of a true representative democracy, I think free speech is pretty well protected in most venues as well as basic freedoms for most Americans.