I really feel like he had aged in Kalos, but I don't think there was any clarification. BUT we do know that in SM he is at least 11, as that is the age minimum for the Island Challenge.
And I thought she was still going for her goal of being a Water type master. She got over her fear of Gyarados and even has a Key Stone and Mega stone for it. Being the Water Type gym leader allows her to continue training and developing counter strategies to type effectiveness which is essential to mono-type trainers.
Pikachu on the shoulder is how it always has been, and always will. A Raichu, while it would be stronger, wouldn't really sit right with many viewers.
Might be the age minimum for the games, though we don't know if that applies to the anime (since, technically, the age minimum for being a trainer is 14 if we go by the games, including RGBY).
As far as a Water Type Master, yes, she never renounced the goal, so she technically is still pursuing that goal, but on the other hand, it is heavily implied from stuff like Whirl Cup-esque competitions as well as her fangirlism to Prima/Lorelei that she needs to reach Elite 4 level bare minimum before she can even come close to reaching her goal. And besides, it's repeatedly emphasized that you need to actually travel in order to reach master level whether mono-type or otherwise, something the gym simply cannot offer. Even Flint, aka, Brock's Dad, made it very clear that Brock staying at the gym ultimately was hampering his potential as a trainer, and that was BEFORE he joined Ash. A more thorough explanation can be found here:
https://www.pokecommunity.com/threads/336960 Not to mention, even in the episode where Misty and Brock did gym leading duties as part of a teaching moment for the class, Brock, someone who was explicitly someone who no longer held the title, did an overall far better job at battling than Misty did. And while it is true that she got over her fear of Gyarados at the gym, and that she has a Mega Stone for it (not sure about a key stone), she would have also gotten them if she actually travelled. And I'll be honest, I'm fairly cynical about the Pokémon Gym thing being equivalent to a Master thanks largely to how much the Gym Leaders were depicted as jokes from AG up to BW. And if I must be honest, Misty even being able to go toe-to-toe with Ash, and actually beating some trainers, even if Brock ultimately did far better than her, was one of the few good parts of SM, effectively redeeming gym leaders far more than even XY did. And I forgot to mention, she didn't even WANT to resume gym duties in GCYL, and heck, literally had no say in the decision (her sisters pretty much forced her to return), and it's heavily implied the only reason she's putting up with it is because her sisters were incompetent. Of course, that might now change soon.
I definitely agree, as I did with Ash, though, that Pikachu's never going to evolve. They had an opportunity to evolve Pikachu again in DP, and he still rejected it.
I don't even see why Pokemon has to be like "the other anime" out there, honestly. If that's the basis for your logic then I'm going to kindly ask you to simply respect my decision because repeatedly telling me that Pokemon should do it because other animes did isn't going to do either of us any good other than going in some pointless circle. I know I'm in the minority and this is one reasoning that is not going to convince me otherwise. And to be fair Pokemon it casually retconning things all the time so them doing so about time is just one of them.
Well, it's certainly more like the other anime out there in the sense that it casually retcons things all the time, I'll give you that much, and not in a good way. Dragon Ball also has that exact problem, as well.