Moving on from the mysterious unnamed Princess who doesn't seem to be around anymore...

Twilight is now an alicorn, and we know very little as of yet from this transformation. We know that she reached it by understanding more about the magic of friendship than anyone previously, which spontaneously caused her to be alicoronated. With some kind of power boost from the Elements of Harmony, of course. Celestia felt the need to shepherd the process, but you get the impression that it would have happened anyway without Celestia being there. Maybe Celestia just eased it along, reducing some of the trauma.

The Twilight and the Crystal Heart Spell, which was originally billed as being canon (but I’m not convinced the writers of the show itself believe that due to how the book and the show diverged on Trixie), has Cadence being a pegasis who became an alicorn by understanding more about the magic of love than anyone previously. We know that these events occurred before Cadence was Twilight’s foalsitter, and she was adopted by Celestia as a niece to officially name her a Princess. From that time to ‘now’, Cadence has appeared to age normally. Her mane also only does the ethereal thing Celestia’s and Luna’s does when boosted by her husband. Interestingly, she doesn't appear to have needed the kind of power boost the Elements of Harmony provided for Twilight for her 'ascension.'

These two have an odd thing connecting them, both 'ascended' to alicorn status by the magic of friendship, or the magic of love. Are there other 'magics' that could do this as well? Can they only happen once per 'item', or is it repeatable? No idea, but if we see any other alicorns showing up, I think we'll find out that they ascended due to some other emotion-based magic.

Celestia has lived for over a thousand years, and given the glimpse of her from the Crystal Empire episodes where she and Luna took down Sombra, has not changed much during that time. She gives the impression of being effectively immortal, if not fully immortal. However, there was a time where she didn’t exist as such, as in the Hearth’s Warming Eve story her task of controlling the Sun (and the Moon when Luna was unavailable) was run by the Unicorn tribe itself. Now, in one of the adverts for MLP, Celestia was referred to as a winged unicorn rather than as an alicorn, so it is possible that when the Hearth’s Warming Eve story said that the Sun and Moon were controlled by unicorns, they may still have been referring to Celestia and Luna, but that they weren’t considered ‘rulers’ at that point.

Lauren Faust specifically mentioned in a Q&A that Celestia and Luna were born alicorns, and if that fact is still true (since Lauren no longer runs the show, and it wasn’t explicitly mentioned in show), then that makes them very different from the ascended alicorns like Twilight and Cadence. It is also implied that Celestia is more powerful magically than any unicorn. However, other than the raising of the Sun and Moon, she doesn’t actually demonstrate any immense magical power. Her defeat by Chrysalis, and Chrysalis’ expression of surprise at that, gives the impression that Celestia’s vaunted magical power is more marketing than real.

Luna I’ve left for last, because she’s the real odd one of the bunch. Like Celestia, Lauren said she was born an alicorn, but her physical age wavers. When taking down Sombra, she has an ‘adult’ or at least young adult appearance, similar to her appearance in Season 2+. However, when she was ‘cleansed’ of the Nightmare in Season 1, she took on the appearance of being much younger, and without the ethereal mane. It's entirely possible that she's actually the same age as Celestia, but whatever is causing these appearance changes is preventing her from matching Celestia. Thematically, having Luna and Celestia actually being twins who's apparent ages are divergent isn't that farfetched. All the twins I know make jokes constantly about who's the 'younger' sibling, and as we will see there are lots of things that may have arrested Luna's development.

There are two different explanations for her appearance changes. The first, and the most popular, is that being stripped of the Nightmare carved off a lot of her natural power as well, and this simply took time to regenerate. The other, which I find interesting, is that her appearance is actually tied to the phases of the moon, the younger appearance being a ‘new moon’, and the older appearance being a ‘full moon’. Although this one very unlikely as her appearance seems to be stable throughout Season 2 and 3, I like it personally.

She has demonstrated some unusual powers, including dreamwalking, as well as controlling the Moon and night sky. It is implied that she controls the stars in the night sky, but it's not explicitly said in the show itself.

Unlike Celestia, we don’t know if Luna is particularly long-lived, because her time as Nightmare Moon throws off all calculations. For all we know, she didn’t age during her time of imprisonment because either she was kept alive by the Nightmare powers, or by the imprisonment itself. I think we can assume that whatever abilities or immortality Celestia has, Luna has as well, but that’s not a guarantee.