Yes, "supposed to", but the representation comes through the voting process, and not everyone votes, so they really represent the voters. And I assume you mean the voters are swayed by the advertising that buckets of cash pay for, since outright bribes are illegal.

The politician who rewards campaign contributors at the expense of voters is thrown out the next election. There's a check or power built into the system, but a lot of the time the new guy is bought off too. Usually the more competition and transparent the industry, the harder it is to buy off a politician. The less power a political office has, the less it will be bought off. There are all sorts of ways to fix this problem without limiting political speech.

Supposed by whom? Certainly, even ignoring ways in which the practice deviates from the overt design, the US government doesn't even pretend to be structured in a way in which all citizens have equal representation.