I would switch between scenarios. (every significant milestone, or around three or four sessions, but mainly whenever the current "dungeon", "book", or "adventure" is done.) I'd suggest taking a look at the books in the series- there are one or two long term issues throughout the books, but by and large each one is a mystery within the book.
What you need to make sure of is that you finish each adventure before handing things over. The villain might not be dead, but he's beaten for now. The city might not be safe, but this particular threat won't be what kills it. (Note: If the bad guys won, which they do sometimes, then that's an ending too.) In the section on cities, it points out that city aspects are expected to change as the game progresses. Basically, whenever one of those aspects changes, and everyone involved in the hubbub has conceded that there's not much more they want to try, then you can safely change. There are a few possibly hiccups.
First, what was the odd character out doing? In Dresden, you all didn't just meet at a bar, so when bad stuff went down and you all pitched together, why did one of you not show up? (That would be the DMs character.) This isn't a hard problem, but you do need to think about it. Did the bad guys start out by neutralizing them? Are they busy dealing with another part of the problem? Are they recovering from a consequence from last scenario? Or, are they right there besides everyone else? (Some people can play a character and DM the game at the same time. It doesn't work very well for me, but if you can pull it off go for it.)
Second, are there any secrets? Is one the the players related to one of the bad guys? Is the big bad working to find the three pieces of the triforce, one each scenario? Are the bad guys secretly breaking the seventh law? Is one of the players secretly a red court infected? (That one actually came up- A player got infected during a session, and hid it effectively for two scenarios. Then we switched DMs when the DM went for a semester abroad, and I had to deal with this sudden new plot thread, and pretending I didn't know when the DM got back. If you're rotating DMs, everyone just has to be okay with the fact that inside of three or four rotations, everyone is going to know whatever deep dark secret they were hiding.)
The best way to fix this is to just not have secrets, but that takes some of the fun out of it. Depending on the players, they could roleplay not knowing. (I love doing that sometimes- the example in the book goes something like "A ghoul snuck in the back window. You failed the alertness roll, so why didn't you notice?") Thing is, just because you're not letting it get transferred to your character, doesn't mean that it's as fun. I love surprises and plot twists, and that is something that gets harder to do as more people share the DM seat. One way to still have this is to have a bunch of bad guys, each with their own separate plots, each run by a different DM. Then again, maybe the big reveal isn't as important.
Another way, if you're all clever at this sort of thing and everyone is cool with it, is to retcon a little when you need. Anything that happened, happened, but you might try something like "Okay, so the first time it turned out Jim Blackhat was a sorcerer. Then next time in turned out he was also a redcourt, but he had been trying to keep it a secret! But now, in his secret lair, you find the true source of his power- He's been breaking the seventh law!" Basically, add your own twist every time the DM seat changes hands. Just be careful this doesn't get too tangled and confusing, and remember not to change anything that actually verifiable happened. Blackhat fell off a cliff, but survived and is back for revenge is probably fine, we shot Blackhat in the chest at point blank but he was a vampire and regenerated might be, but around the time the players burn the body and douse the unmarked body in holy water, he does not come back. That's why evil villains have apprentices anyway!
Third, all characters get access to all milestones, even if they slept through the whole thing. That sounds a little obvious to some, and wrong and unfair to others, but especially if there are a couple of significant milestones or even one major milestone, you need to give it to all characters. Playing more than a few skillpoints behind, or even one refresh behind, is an irritating shift in power and agency. Your mileage may vary on that, but it's not hard to come up with a story to justify it if you need.
In the end, it works out pretty well. Just realize that you are giving up a certain level of genuine surprise and twist to the story, and the rotating cast will feel a little different than the same tight nit team every time.
I would say this is bad practice. You've just had the players roll alertness when they should be rolling empathy. Say one of your characters has Empathy as a Superb skill. They get a huge bonus on the roll. Say they also have only an Average Alertness. You've just denied them a +4 on that roll and they don't even know it! (If they find out they will be rightly angry.)
If you want to test a skill without the players knowing you can always roll for them in secret. That way they have no idea what you are checking against merely that you are checking for something.
However in a system like FATE where players can spend FATE points to modify rolls, etc I wouldn't even do that. I'd have them roll empathy, you don't necessarily have to explain the roll but that lets them leverage their stunts, powers, and aspects as per regular play. If the players figure out what's going on but fail the rolls then their characters are still in the dark. If the players have their characters act on player knowledge you can gently remind them that their character is blissfully unaware of the problem. It can make some interesting tension in the game the same way you don't want a person to open that door in a horror movie! Roleplaying is partly about being able to separate player knowledge and character knowledge.
Best Answer
In the Fate Core rulebook, there's a section called the Veteran's Guide on p.294. That's a good place to start for differences, but it turns out it's even easier than that. On the G+ Fate Core community, someone compiled the rules changes from Fate Core to Dresden Files.
I thought this was rather light, but after playing, I can tell you that this distilled document is pretty much the complete list of changes, though one bit did throw me off. In the document, its stated that spin is no longer optional; it's a bit simpler than that. I suppose that the author was trying to define things so that people could see it using completely the DFRPG rules. That part is actually distilled down to the fact that there are four outcomes (which distills spin). There is also succeed with a cost, which definitely has opened up some avenues in my own experiences in Dresden Files.
There's also the simplified actions- those being Attack, Defend, Overcome, and Create an Advantage. A couple of things that were also left out from the Veteran's guide - the fact that aspects can be invoked in new ways: teamwork, to give another character +2 to roll vs. relevant opposition, and most importantly to me, to create or fortify an obstacle, i.e. give +2 to active opposition, or create opposition if it was not already there.
A couple of things that are left out which we had already started using, but others may not have. Zone borders are replaced by situational aspects. This is very important, and we had started to use those in any case in my game. What this lets you do is play without maps, and it's very helpful in other realms, as I found even defining zones when in the NeverNever to be a bit limiting. Supplemental actions and skill modifiers are removed- and we'd already done so.
There's also one rule from Fate Core that I did institute to help even more. I found that the focus on fewer aspects in Fate Core was definitely a good change, and after talking with my players, we were able to pare down our aspects. They didn't begrudge the change, and it didn't really limit them, but it does take conversation, as it does, on the surface, seem like you're losing something.
As far as whether it's worth it, in the end, I've made several other changes that fit together with Fate Core a lot more, so it was definitely worth it to me. In the Pros columns just in general, Fate Core is much clearer and definitely better written IMO. In the Cons column, there's a lot to Dresden Files that isn't really in Fate Core, so you're going to need two books for rules. But other than those two details, it really depends on what you're comfortable with. There's no inherent dissimilarities that would make it a no-go, and I think that was done on purpose. Even though Fate Core is said to be the ground zero of a generic Fate system, it really is iterative, and there aren't really any incompatibilities that I've found.
UPDATE: Looking at the additions in the question, there are some interesting ideas there. But other than a couple of things from the skills, I probably wouldn't use them. In the end, my particular flavor of Dresden Files has gone more narrative. If I don't need it for the narrative, I don't sweat it. Both the tweaks and the Evocation seem like they add a lot of complexity for its own sake, when Dresden Files is already complex enough. And they don't really add anything that the ballparking it from the rules of Fate Core and ignoring the rest do. For example, the rules about moving zones haven't really come into play a whole lot in my game- mostly because the whole zone thing has been one of the weakest parts to me. The situational aspects of the scene help a whole lot more with making zones narrative, and since adding them, my RCI (Red Court Infected) in my game has actually felt a lot faster as opposed to the movement through zones, and the others have actually not stumbled over the use of zones as much- it's just organic now.
There are some good ideas in there- I'd just try to look at the flip side of what you're giving up. Fate Core to a large extent is just more intuitive to me. And in taking that same philosophy in my translation and in my moderation, things have started going a lot faster since I've been integrating them, and we've made a lot more actual narrative progress.