Even though in more recent years, each mainline game seems to go out of its way to give "Zelda" a unique personality separate from the other incarnations, she's still largely the same character in every context. And while it isn't true for every appearance, often there's an in-universe explanation for the different Zeldas and Links suggesting they're either descendants with a blessed bloodline or even literal reincarnations, so there's usually at least a tangible connection between them all.
Impa, however, doesn't have that, and she differs from game to game far more noticeably, varying wildly in design, personality and prominence within the story. This is more like Cid, who is always connected to airships and machinery, but otherwise is always a clearly different character.
And as an aside, it's always been interesting to me that Impaz, from Twilight Princess, isn't usually counted as one of Impa's appearances, just for having a Z in her name, even though she has just as much in common as the rest of them do. In my opinion it shows how tenuous the connection between the different characters really is.
Yes and no. No and yes.
Impa has 2 distinct roles in the Zelda franchise.
One is as Zelda's personal bodyguard, which is the role she started out with in Ocarina of Time. And later also took on that role in Skyward Sword, albeit for different reasons altogheter. Both these Impa variations are fastly different, but they share a common goal; protect the Princess and guide her towards her destinied goal.
Which is also what Old Impa does really. She's mostly a nurse maid to Zelda, incapable of being a personal body guard due to her age and lack of strenght, but important to her still especially for her wisdom. This wisdom is still seen in variations of younger Impa, as OOT Impa trained Zelda to be Sheik and was the Sage of Shadow, and in Skyward Sword, Impa grows from a fierce, independent and impantient warrior to a wisemind in her older incarnation as the Old Woman. And in whatever role she's in, she was always been the Sheikah leader, or one of the few survivors of them.
If you compare this to a princess who's also been a Sheikah male cosplayer, a pirate leader, a spirit guide pocessing a overly large armoured knight, a mere student in the Knight's Academy and Link's childhood friend, then there isn't all that much inconsistently. Aside from the design choices yes. And obviously age and combat-viability. But one new appearance could change that around if they want the character to fully establish itself as a Zelda-mainstay. Which is why there's still a chance she can be picked as one of the DLC characters if Nintendo is already making plans for a BotW-prequel featuring a Young Impa.
I really doubt the Sheikah-theme is going away from Zelda if the lore of BotW is build upon from, something they also did with Ocarina of Time and it's lore expanding towards Wind Waker and Twilight Princess most noticably (also Skyward Sword but to a lesser exctint because it's the beginning of the Zelda lore). There's a lot of backstory which BotW hardly addressed like the Sheikah vs Yiga rivalry, the beginning of the dominance of the Sheikah race, the true origin of the Calamity and how Ganon(dorf) found this power, the Yiga swearing alliance to Ganon, the King of Hyrule forcing the Sheikah to exile? All major plotholes that can be picked up from, and since Impa is STILL the leader of the Sheikah in Breath of the Wild, that would mean she's the leader in the past as well, and since she also reincarnates all the time, she would be the same Impa even in a past further than a direct BotW-prequel.