You can cancel an award ticket at any time prior to departure and for any reason. You'll get your miles and taxes back. If you cancel after you check in, the refund is not automatic. You have to call and the agent will handle it manually.

As noted above, if your flight is delayed the app will often present you with alternatives to your final destination, especially if the delay risks a misconnect. Otherwise you can call and will be reaccommodated without a problem. It helps to have alternatives ready to suggest. You should not be charged any extra miles.

If you're at a connection point and your onward flight is delayed significantly, to the point where the trip no longer makes sense, you can see an agent and declare a "trip in vain". This is where it becomes somewhat discretionary but you may be able to get them to rebook you back to your origin and get a full refund. I haven't needed to do this in some years, so I can't say you can expect this. They can certainly send you back to your origin but the refund may be tougher. Can't hurt to ask upfront, or after you're back home.

If you're at a connection point and your onward flight is delayed or cancelled and you want to continue, then it's pretty standard delay treatment, irrespective of whether it's an award ticket. You may be offered alternatives via the app, or you can just stick it out. Be sure to get a straight answer on the cause of the delay. (I consult the flight status on ExpertFlyer.) If it's mechanical or some other cause within AA's control then push for hotel room, meals, and/or rebooking on another airline. Again, you should not expect to lose any miles or have to shell out any more.