1 - It won't be at similar pace if in a deficit - you'll lose more fat than muscle you gain, so weight does drop because of being in a deficit. But yes, that's what is happening. Same way your body still replaces skin while in a deficit - which means it's building new skin basically, or hair. Both of which can have problems if you undereat too much.

2 - Yes real. Depends on how long it takes to tap out your existing muscles for everything they got, and then however long you got to 9-12 months lifting that would be the beginner stage.
It's along the same lines that someone at maintenance or even surplus will gain muscle faster as beginner - body is just ready to grow, and easier to overload.
Past that first level - both those are harder to accomplish, no matter where you are eating - but especially in a deficit.

3 - First improvement from exercise is water weight gain for many reasons, and that is fast. Muscle is slow. For a woman eating in surplus doing progressive lifting - 1 lb every 4 weeks.
You can lose fat much faster than that.
It's popular phrase to throw out that has no bearing in reality.

First week or two included water weight, so knock those off, then look at rate of loss.

You can increase strength without new muscle. Form improves. And you start engaging the whole muscle totally, Central Nervous System improvement (CNS).
Once those 2 things happen, and you keep overloading - now the body needs to add more during the repair.

Soreness eventually goes away, but it's a good indicator near the start. You damaged muscle fibers, they repair stronger if diet allows, more if needed. You are sore the next 24-36 hrs.
Later the soreness may go away, but the time is still about the same if you overloaded.

So very much a newbie. Maybe 1 lb every 6 weeks if that.
Again, size and strength doesn't mean you built new muscle. Size is increased glucose stores with water, and less fat on top showing it off, strength means better form and CNS engagement if you do it often enough. But ....

Are you totally switching up workouts, or merely what the lifts are?

If lifts or rep ranges - that means some of your time is spent trying to find the right weight for the reps, and you can get sore from different rep ranges. It also means for the weeks trying to find the right weight - you really aren't overloading. And then you are spending time using your whole muscle by getting form and CNS down again.

If you aren't doing anything long enough to keep overloading it and making progress - you aren't building as much as you could.

Getting sore because of changing routine and working out new support muscles isn't the same as progressive overload requiring new muscle.

Are you switching up routines based on the mistaken myth you must "confuse" your body to keep seeing progress?

How long they last is totally up to you. When you can do the rep and sets and not have any difficulty - you are maintenance lifting.
And at that point you could actually do about 1/3 the duration and 1/3 the frequency that got you to that weight - but you'd have to keep the weight on the bar. But that would be maintenance lifting then, like if time got busy, other workout desires, ect.

1 extra pound fat loss masked by 1 lb muscle gain in 6 weeks isn't much, that's almost water weight fluctuations - but it could happen.

And I'm estimating 1 in 6 - because normally for newbie woman eating in surplus it's 1 in 4, at maintenance it's going to be slower by decent amount.