Yeah, people who survive long enough to get there. Some accidents will always happen.
Right now, yes. That doesn't have to be the case in the future. What if we used nanorobotics to heal our injuries, or at least keep us alive long enough for help to arrive? What if we somehow used quantum entanglement to teleport? What if we uploaded our minds to a computer, and our bodies were disposable?
Obviously none of this is possible right now, but we're talking hundreds of years in the future. Even if accidents happen, they probably won't kill anyone.
AI will screw up rarely, but it will still need humans telling it what to do, there will be unpredictable things now and then, etc. There will be some screw-ups.
Well, no. The ultimate goal of AI is to create an Artificial Intelligence. It won't always need humans telling it what to do. And if we eventually manage to create an ASI, it won't make any mistakes at all.
For now. Nationalism is a more powerful force than you think. People might want to secede. There might be some hang-ups over national honor. There could be a competition for domination for space. Wars could get rarer but I wouldn't completely rule them out.
In a world where everyone is unaging, death would be taken very seriously. I'm sure nationalism would be around, and there may be competitions between countries, but I doubt there would be any deaths. Even if there were wars, they'd probably be cold. Even if they weren't, why use people to fight? A drone is a hundred times more useful than a person is in war.
A huge portion of people who will live to see life extension will lose relatives beforehand. Pretty much none of our grandparents will see this. Many people will lose their parents before, they will lose other close family as well through various accidents or disease.
People have lost relatives since the dawn of mankind, yet vast majority never commit suicide. Even if some people do, it will eventually stop. The people who lost someone before everyone became immortal would very quickly become a minority and either move on or take their own lives.
In the end, only people who want to live would be left. These people would never have any reason to die, since it's now next to impossible to be killed.
And, like I said, anti-depressants or neuromodulation could help the people who are in pain from having lost their loved ones. I wasn't kidding when I said that depression might very well cease to exist.