You can move freely between cities at any time of your choosing, if you have access to roads. And you really just don't have access to them in "dungeons", but then again, you can just backtrack out of them in most cases. That means you can go back to your camp or another location when you choose, albeit with some work in some situations.
That means that yes, once you're done in Lothering, you can head to Denerim, do the business you want there and then head to Redcliffe without having to complete Denerim. And then you can go back to Denerim whenever you want. And go back to Redcliffe if you choose to. And go back to Demerim, etc.
Be careful about when to leave Lothering though:
Lothering is the only city you cannot go back to once you leave as it is completely ravaged by darkspawn. It will still show up on your map, but the icon will be a skull. Finish every quest you can find and pick up everything you might want.
Some specializations can be unlocked through the purchase of manuals. Most of them can be taught to you if you befriend the right party member. Those specializations are:
- Berserker (Denerim, 11 gold) - Can also be taught to you
- Reaver - Only in Awakening; has to be taught to you in Origins
- Templar (party camp, 15 gold) - Can also be taught to you
- Assassin (Denerim, 11 gold) - Can also be taught to you
- Bard (Orzammar, 14 gold) - Can also be taught to you
- Ranger (party camp, 15 gold)
- Blood Mage - Only in Awakening; has to be taught to you in Origins
- Shapeshifter (Dalish camp, 12 gold) - Can also be taught to you
- Spirit Healer (Denerim, 15 gold) - Can also be taught to you
Duelist can only be learned from Isabella in Origins. However, I'm not sure if this was a bug or not, but during my last playthrough, I unlocked all the specializations by playing the Golems of Amgarrak DLC campaign in the middle of my Origins run and importing my warden to the DLC. All specializations were unlocked for that campaign and remained unlocked when I went back to Origins. I don't particularly recommend doing this, mostly for story-telling reasons, but if you have the DLC, this might be a way to unlock specializations. Assuming I did not have a special bug on my game.