Before phoming to cancel you really need to look at other options including reroutng and put those to AA and see what they say. You don't just have to accept what AA have done or take a refund.

That might include (and this is based on the CUN wiki page so these options may still not apply) the direct BA LGW-CUN flight or sometining like Iberia via Madrid or if you want to stick with AA then routing via other AA gateways such as JFK or ORD or MIA rather than DFW.

If you want to rebook via an OTA then you'l have to take the AA refund option.

Yes BA charge to select seats on BA operated flights. Exception is if you have status. BA fees apply no matter who you book with.