Yes, you can. I typically choose specs for roleplay reasons, for myself and followers.
Your decisions seem similar to mine, but I have a few different ideas. I use Awakening in the OC, so I can use the Awakening specializations as well in the base game. Anyway:
My PC: either duelist or shadow, depending if he or she is a close-quarters reckless rogue, or a in the shadows, trap and bomb-using rogue. Either Champion or Reaver, depending on what kind of warrior he is, tank or DPS. Shape-shifting Blood-mage or Shape-shifting Arcane Warrior, depending on race (human or elf) and predisposition. Why double? Because I use a mod that swaps the spider-form for the wolf-form. Wolves>Spider,
.
Oghren - I respec him into axe-and-shield Beserker. Same in Awakening. Lore friendly and game-play wise better for me: one more tank. I dislike having to wait for the corpse in DAA, since I do Blackmarsh last.
Sten - Reaver works as well. The description makes no sense, since I feel they retconned the specialization later on. There are no demonds, you just drink dragon's blood. Me and my warriors have enough dragon's blood to go around after Kolgrim gave us the vial to poison the Urn. Doesn't matter that we double-crossed him and killed him and his toadies. The vial alone is worth more than any treasure (since I can RP using it to give Sten the Reaver spec, or save it up for later if I want to defile the Urn or not).
Alistair - gets templar or champion. He was trained as a templar, but the lyrium problem is awful. So I usually make good use of his templar skills at Redcliffe and the Tower, and after that I respec him to be a Champion. He quit lyrium,
Leliana gets only bard for story reasons. Archery with bombs and traps and maybe sneaking (she can backstab with one dagger just as well, not as efficient, but I usually don't give her dual-wield).
Zevran gets assassin. (I always romance him, regardless of Origin. He's such a cinnamon roll
). He's a beast with dual-wield, bombs, traps and sneaking.
Wynne gets spirit healer.
Morrigan gets shapeshifting, yes, but I feel like post-Brecilian, Arcane-Warrior works as well, since it's elfy magic, and she already has elfy-magic, and is interested in elfy-magic. I usually give her some mage-appropriate armor from Loincloth-Fashion, Spellweaver, and a Dar'Misu dagger with a few runes. I switch between close-quarters slashy-mage or long-quarters WMD. Both feel appropriate for an apostate who lived her life in the forests and marshes of the cold South, unlike the squishy circle biddy.
Anders gets blood-magic and Arcane Warrior. We learn that he's always been interested in healing, yes, but he can heal fine enough with just the Creation spell. While the "spirit" part might be more appropriate in DA2, I don't like to think that I had any thing to do with... that. But using blood-magic to make him hate it? Yes please. Plus it's the only time a companion actually comments on it. Why Arcane-Warrior? I'm training Wardens, ergo they need to pull double duty as casters and tanks. Same for the other mage. It makes even more sense for her to either get shapeshifting or Arcane-warrior.
-- DA2 --
On a mage PC Hawke, I take blood-magic pre-Leandra, force-mage post-Leandra. My apostate uses notched sword and marcher shield (yes, mod that removes weapon style restrictions, but not attribute restrictions). Hey, I'm not going through Kirkwall using staves and spells. Neither is Anders or Merril. I make my mages use other weapon styles (because apostates) and wear other types of armor (DLC armors look nice, and apostate-y. I use Diversified follower armors, since I find the idea of some characters not changing their clothes in years disgusting.
Looking at you Inquisition Morrigan.)
All of the followers have their fixed spec, yes, but I use a mod that unlocks all class appropriate skill-trees. In other words Isabela can use bows, Sebastian can use daggers and axes, Carver and Fenris can be SnS tanks, Merril can get creation, etc. It's not lore un-friendly. We had this choice in DAO even in vanilla consoles, without mods. We could ignore the points used by the game, and invest the rest in to whatever style we wanted (SnS sten, Dual-Wield Alistair, etc). I don't like the direction Bioware went with DA2, limiting player-choice when it came to skills, weapons and armor for companions. Thankfully mods exist to fix the game, ala Bethesda.
-- DAI --
Didn't play it yet, my laptop is a toaster. Saving up money to upgrade some day. Maybe I'll wait for all the DA games to come out (after Dread-Wolf Rises there's supposed to be another one, right?). In any case, I don't care about spoilers, since I can enjoy a story just as much without playing it. Plus I played a few minutes on a friend's Playstation. So I have a pretty good idea what the game feels like.
F!Mage solasmancer: CAN'T DECIDE!
M!Dalish Mage: uhhhhhhhh, Knight-Enchanter?
Rogue: Assassin.
Warrior: Champion.