Yes US pilots are welcome at CX. Having spoken recently to a manager involved in US recruitment interviews the problem is finding some that know anything about flying big jets. (no offence to you)
Age limit for S/O is somewhat flexable. 36 is published but age / experience comes into play at the upper level.
Can't say what the "competitive min's" are as I'm not that sure.
Medical exam is thorough but nothing more. An AID's blood test and liver function test will be done. At low 30's you should be in reasonable shape and that's what they want to see. You'll have 20+ years to get out of shape!
One word to the wise though. If you get an interview don't repeat what you have written here. ie "just one of those life experiences I'd like to try out while I'm single". You won't get a look in with us or any other airline if that's your attitude. Big investment requires a return past your single days. If it's still your attitude keep it to yourself.
I expect you will have to work a while more with the age v's hrs but if CX is your goal, good luck. (you might need it)