Flemeth definitely calls Mythal an ancient being, rather than an ancient elf. Abelas also says in his hidden writing that those who came after the Veil are faithful to Mythal but "do not understand what she was in her fullness". Again this is an odd way to talk of someone who was an elf such as he. I don't think that reverence comes just because she placed herself at the head of the pecking order; she was different and superior in what she could do.
Solas at the beginning of DAI is not the same as Solas in Trespasser. He says when he first awoke he was weak. How many mages do you know who can turn someone to stone permanently without even looking at them? Solas was also capable of a great deal more in the past. He did after all create the Veil. We don't know if he did this alone (probably unlikely) but this was reality changing magic. Most of Corypheus' power came from the orb, an elven artefact.
I think the whole point about the ancient elves and the Evanuris in particular, is that they were different creatures from modern elves. They were the People, the Elvhen. It would be more correct to say that was the starting point and modern elves are what they became.
If you look at the statues and pictures of the Evanuris they look strange, almost alien. If you look at the statue of Mythal I wouldn't automatically look at it and think she was an elf. The Evanuris can adopt different forms. They also warn against the "forms of Fen'Harel". The guise of the humble wanderer is just one of these. He may claim that he was Solas to begin with but that doesn't mean we are actually seeing him in his true form.
But ancient elves are ancient beings. One does not exclude the other. I agree with you that they were more than what modern elves are thanks to Solas mucking things up with the Veil, so if she had just said "elf", she would have had to blurt out a bunch of exposition explaining this distinction between modern elves and their ancestors, and also how the Evanuris came to attain godhood. Which is explained in the game anyway, just not through Flemeth. Perhaps Flemeth didn't want to be specific or ruin the mystique of the Evanuris? You also have to bear in mind that:
1) Abelas is a slave of Mythal, he worships her. It's normal that he would have a larger than life view of her. Solas, on the other hand, is a lot more humble when he talks about himself and his Evanuris buddies.
2) The modern elves know extremely little of their true origins and their true history. They also know almost nothing about the true nature of their gods. Most of what they know is mired in myth. For example, they have no idea the vallaslin was a symbol of enslavement akin to markings on cattle. They have no idea how the Evanuris really treated the elves of old, and so on.
Solas is the same Solar throughout, he is just weakened by the uthenera when we first encounter him. But it's not like he's a different being. Like I said, him being very powerful does not make him not-an-elf. Ancient elves had a completely different relationship with magic than anything the mortal races have been able to achieve, so such a being would appear mysterious and god-like to mortals. And this happened partly because there was no Veil to separate them from the Fade, and partly because they lived forever and had ample amounts of time to perfect their knowledge and skills.
We know since DA:O that elven society massively regressed when they lost their immortality. The elves of old are the ancestors of these regressed remnants of an ancient empire, but they're still elves, which was my original point. Arguing they're not really elves would be like arguing the ancient Egyptians weren't really Egyptians just because modern Egypt is a pale shadow of the empire it was 4000 years ago. They were elves then and they are elves now, it's just that their civilization suffered tremendously and was nearly wiped out.
To address your final points, shapeshifting isn't really that odd in the DA lore. It's a rare school of magic, but completely doable, even by mortal mages. So the fact that the Evanuris are sometimes depicted as looking like animals isn't strange at all.
Secondly, bear in mind that ancient art is often stylized, not realistic. Take the Easter Island heads created by the Rapa Nui people as an example. They depict human chieftains, but they look "alien-like" as well. You could argue the same is true about the old statues of Mythal & co.
If the Veil is removed, it stands to reason that the modern elves would go back to being how they once were - immortal and completely attuned to the Fade / source of magic. At least that is what Solas believes. (and Sandal) Their current mortal state is not natural.
However, considering how crappy Solas is at gauging the outcome of his spells, removing the Veil could very well destroy everyone, the elves included. This plays into one of the running themes of the series - that simply being very powerful does not automatically mean you fully understand your power.