how can I show that twenty years have past?
Since you're only intending on using the +20 years time period as a framing device to show the importance of the story to the character keep the "future" segments focussed as much as possible on the character rather than the future setting itself. Ideally you'd show only that which is explicitly necessary or anything you want to foreshadow - for example if the character ends up in prison as a result of the events of the main story you could show them in their cell, or just being released, or if they lose a limb you could show that. In general you can show the passage of time more internally - they could feel some typical old-age symptoms, or you could have them see themselves in a mirror and see grey hair. That sort of thing coupled with a simple mention of the timeshift back to the main story is more than sufficient.
You can have them telling the story to a third party but this isn't strictly necessary - you could just as easily have them narrating the story to the reader, if anything I'd suggest doing the latter unless you have a reason why the third party is relevant to the story in someway (such as recounting important events to pass them on to a descendant).
how "futuristic" should these beginning and ending scenes be?
Taking the approach outlined above means that this question becomes largely moot - you shouldn't need to show enough of the setting for it matter, and if you are then it's probably a sign that the beginning/ending scenes are becoming too overblown and straying from their purpose.
If you find yourself running in to that it's time to take a step back and ask if you really need to be showing what you try to describe, whether doing so actually serves the story you are trying to tell. If it doesn't then cut it - otherwise it will only serve as a distraction to the reader, and on the extreme end of things only serve to leave the story horribly open to feeling dated, try looking at anything set in 2020 that was written 20 years ago and you'll see what I mean.
should they refer to present day technologies as if they're antiquated, and should new technologies be mentioned?
No - there's some argument for doing so if they are telling the story to a third party that would view them that way, and in that case a handful of references early on just to establish it can work but honestly I'm not a fan, because even in that situation the third party is essentially an audience surrogate and talking to a contemporary audience about their "antiquated" iPhones etc is just plain irritating. Instead have the main narration in what is essentially contemporary past tense, it's easier to create and maintain immersion in the main story that way. You want the context of +20 years at the beginning and end for the perspective but other than that let the main story fly.