Here are my two cents, for what they're worth.
I didn't really enjoy DA2 as an overall game, but then, i was constantly comparing it to Origins. I think if i'd played DA2 first, i would have enjoyed it a lot more. DA:O, to me, is one of the best games i've ever played. I've played it through at least 15 times and i'm still not bored of it. I've just bought the Ultimate Edition so i can uncover even more!
There are a lot of things i would change in DA3, but i'm sure i don't speak for all fans when i make my suggestions, they are just what i would like to see in the game
Story and Play
I would like the story to involve the original Warden and companions from the Origins game (personal preference) and involve them rebuilding the Grey Wardens. In order to do so they would need to travel to a number of places mentioned within the game, such as Orlais, Antiva, Tevinter Imperium etc. I remember reading somewhere that developers were looking at Skyrim for ideas. That game is massive and having a good number of different areas to explore properly, would be great.
Players should also be able to transfer over their save file from the first game and just carry on (as touched upon in the second game)
I'd also like the Warden to travel back to Highever (if they chose the human noble storyline) rebuild it and install Fergus as the Teryn. It could be done as a side quest. They could also discover who, if anyone, survived the massacre. Such as Ser Gilmore (personally i'd have him survive)
I understand what they were doing with DA2, but i think a good number of fans were disappointed in the extreme change in gameplay. I know that the Elder Scrolls games change with every new one, but the idea and concept of the games remain the same. I personally felt cheated out of a proper ending... the Warden just disappeared and was merely mentioned in DA2. I love my Warden, i hate Hawke.
I know i don't speak for every female fan, but please, please, please... bring back Alistair as a companion and romance candidate... everyone else just falls flat!
I did and didn't like having a voiced character. I liked it for the extra depth it brought to the character, but hated that it was only available to humans... at least make it available for all races!
I also like the idea of choices and having them influence and shape your character. It was touched upon in the DA2 game, but not enough. Look at the Fable games and how it works there. Literally everything you do shapes how your character will be and this would be a great element in Dragon Age, especially if you're going for the voice option.
Deeper and more realistic romance options would be great. The option to get married, have or make an enemy, it would be great. If you carry your save file over, you can marry the companion you romanced in the first one, for example. I wouldn't go as far to say "give us children", but more realistic developments with romances would be great!
Speaking of companions, please, if you do change them, make them like they are in the first game. They are deep and meaningful and add a LOT to the game. I loved discovering new things about companions, uncovering their quests etc. It could be taken further and players can uncover even more about the companions they choose to play with.
Also, please scrap the "i can only talk to you at a certain point in the game" model used with the companions in DA2, let us talk to them whenever we like, as in Origins... Give them all a camp or a house... but i like to be able to my friends whenever i like, not when the game dictates.
I prefer the map from the first game, please bring it back! In fact, i prefer the whole inventory setup from the first game... bring that back too
Can we have Mabari's back?
I hated the mage/templar storyline... it was just bad. I liked having a nemesis and a purpose to do things. As the story developed, i became attached to my warden. What happened to her family made me sad, she fell in love with Alistair, so did i, when she finally got vengeance for the massacre of her family, she felt great, so did i. I didn't feel this in DA2.. i hated playing Hawke, i didn't feel connected to her. I felt like i was watching someone else play the game, like a bystander. It was just awful, i don't know how i endured it to the end!
Deeper, longer, more meaningful side quests. Ok, they're only side quests, but the ones so far have been pretty easy and a bit nonsensical, they remind of the started quests in Warcraft, they don't add anything to gameplay... a revisal of these would be good

Maybe more race, origin and class choices
Combat
I prefer the combat in the first one, even if it was a bit slow and clumsy. The second one feels a little arcadey and too fast at times. I also think the talents were far more complicated than they had to me, they may have been easier if they had the same interface as the first one... the talents were miles better, but i HATED how you had to choose them!
I do however prefer how the mages play in DA2, they are way more fun to play than in Origins. I love that i can cast an arcane bolt or whack someone over the head. I definitely think the mage way of playing in DA2 should be kept. A good mix between the two styles would be great.
Environments and Effects
I love how the game looked in DA:O, but not so much in DA2. I can't quite put my finger on why, something just didn't feel right with DA2. I think looking at how the environment is dealt with in Skyrim would be an idea. The environments there are phenomenal. I like the idea of weather, should be brought into the new Dragon Age, as well as breathtaking art.
People like games that look amazing and the effects really could do with some work. Especially the characters and how they look. You only have to look at some of the mods available to see how different a character can look. I like my characters to look realistic and to be honest, some of the characters in DA just scared me, especially Loghain...
More dungeons and places to explore are a must! The one thing i hated in both games, was the limited world! Coming to the edge of something and bumping into it, annoying! Please, if you're studying Skyrim like you say, take a leaf out of their book and give us places to explore!! They don't need to be quest related, but could be a good way of adding epic weapons and armour and other items!
A better quest journal, i found both quite difficult to navigate (being so used to the Warcraft quest journal which is amazing)
Weapons and Armour
It's hard to say which sets i prefer. I think the Templar armour is my favourite and i liked being able to customise my companions in Origins. I think both games need more varied sets, especially with regards to mages. There just wasn't enough staff or armour options in either game!
I think that's all i have for now... excuse the HUGE wall of text, but i have a lot of ideas. I'm passionate about the Dragon Age series and don't want to see it getting worse with every game that comes out. I have so much love for Origins, it's familiar to me and i play it so much! It's sad that i've only played DA2 through once and sold my copy, i never intend to play it again. I want DA3 to be like DAO, i want to be able to play it over and over, discover every ending, every story, every companion... everything! I want to be able to waste hours and hours and not regret it. I wish i was a writer on this... i just hope they've got David Gaider as lead writer... that man is AMAZING with stories...