Indeed. Good luck arguing in court that someone gave up their right to sue. The legal profession tends to be awfully sceptical of such measures, and none more so than judges.
Umm, no. IANAL but even basic research pulls up the Federal Arbitration Act, which was passed in 1925 and allows for contractually-obligated compulsory and binding arbitration, and this has been held up in court time and again. The only way out of this is to prove the company is using a biased arbiter (they basically all use approved, neutral 3rd party arbitration services now so good luck) or (as you yourself speculated) if the clause isn't applied equally (ie. if the company still reserves the right to sue YOU - but unless they're stupid, they don't make this mistake either). TFA even points out that mandatory arbitration clauses have surged in popularity since the Supreme Court ruled in 2011 that it was okay to use them to suppress class action suits.
The thing that might (I sure hope) make the "contracts" discussed in TFA unenforceable isn't the fact that they make people give up their rights to sue, but the fact that some "legal terms" page on the company website that the consumer probably isn't even aware of (much less has read) does not a binding contract make.