Within 50 years (if not much sooner), we'll almost certainly have cured aging.
Well, there are some folks who know a lot more about medicine and biology than I do who believe that, but it's far from a certainty. Note that the average and median life spans for people have increased greatly in the last hundred years, but wake me up when someone makes it much past 115. Those outliers have been around since antiquity, there are quite a few in my family tree from centuries ago (an uncle was into genealogy).
I'm 60 and already starting to feel the effects of aging. I'll be 110 in 50 years. I'm pretty skeptical, they're going to have to figure out how to extend telomeraise (I don't know how to spell it, and neither does FireFox) without giving you cancer. They're going to have to figure out how to stop genetic errors when cells divide, and quite a few other thorny problems. I doubt my ten year old great nephew will see it, let alone me, and it may be an impossibility.
Once you approach even half the speed of light, local time slows down for you, so e.g. a 50 year trip would be 'only' 30 or 40 years (I haven't done the exact math)
Unless I'm mistaken the math is straightforward; at C the trip would seem instantaneous to the traveler, so half C a 50 light year trip would seem like 25.
But then, there's the problem that time speeds up greatly as you age -- remember how far apart Christmases were when you were five? That phenomenon accelerates as you age.
the goal of sending autonomous robotic explorers to stars (a la Mars Curiosity) just 13ly away may be quite feasible in some of our lifetimes
Certainly we'll have robotic probes to the stars in a few hundred years, but I'm very skeptical that you'll see it in your lifetime.
we take for granted, may change dramatically - e.g. the typical human lifespan.
The typical lifespan already has nearly doubled, but the longest lifespan hasn't changed at all.
Also, perspective: We've been 'human' for approximately 2 million years. We have millions of years ahead of us as a species, and even on cosmic scales, you can do an enormous amount in even just 2 million years.
I'm cautiously optimistic. I think our future in space is practically certain, and that we'll probably ultimately reach hundreds of other stars, and establish colonies on other planets. It's a matter of when and how, not if.
That I will agree with. I'm in the middle of writing a sci-fi book set ten million years in the future. In the book, we have evolved into at least four separate species (there may be more, I never know from one chapter to the next what's going to happen), one on terraformed Mars, one Terraformed Venus, and two on Earth. The Earthians have time travel, FTL travel, and a 500 year old is a young man. If you're interested, here's the first chapter. What's done so far is all posted (if you hate it, blame slashdot! They started it...).