I'm as yet unpublished in the PB department, so take this with a grain of salt, but I've read a lot on the subject, so I'll share what I've gleaned. (If more experienced authors find errors in what I have to say, please feel free to correct me).
So first off, there are three basic ways you could get paired up with an author.
1) An author hires you directly to illustrate a book they intend to self-publish. They're essentially your employer.
- In this scenario, all bets are off. They could give you lots of leeway or micromanage until you want to scream. You'd have to work that out between the two of you.
2) You and an author decide to co-create a book, and then submit it to publishers as a package deal.
- First off: THIS IS A BAD IDEA. That's not to say it's impossible to sell something like this, but it presents a lot of problems to publishers, who may really like the illustrations but hate the writing, or vice-versa, or they feel like they could work with one of you, but not the other. Publishers like the opportunity to pair authors and illustrators themselves; maybe that new, unknown author will get a boost from being paired with a well-known established illustrator, or vice-versa, or maybe they simply know someone who's extra-talented at drawing children, or animals, or moonscapes, or whatever the topic of the story is.
3) A publishing house approaches you and proposes you illustrate a manuscript they've recieved.
I'm going to assume you're talking about this third scenario. In this instance, the illustrator is generally given a lot of leeway in what to draw. Writers may put "illustrator's notes" in their manuscripts, but a writer who tries to dictate every detail, down to the color of the buttons on Mr. Fuzzy Slipper's shirt, is going to get shut down. "Illustrator's notes" are generally restricted to things that are important to the story, but not explicitely mentioned in the story. (e.g. The manuscript says, "Look! A kitty! I think I'll pet it!" and the illustrator note might clarify that the "kitty" is actually a grumpy-looking lion).
Beyond hitting those larger points, it's my impression that illustrators are generally encouraged to follow their own vision of what the story looks like. Many PB illustrations are straightfoward depictions of the story and there's nothing wrong with that. However, it's not uncommon for the pictures to contain a second, silent story only tangentally related to the words, and for the most part, it's encouraged. Kids LOVE looking at the pictures and discovering a second story behind the scenes.
So if you're worried about being micro-managed, I wouldn't be. If a publishing house trusts your artwork enough to take you on in the first place, they've already decided to put their faith in your abilities. They may tell you how to break up the story "e.g. this line is the big reveal and needs its own page," kind of stuff, but probably not much more. (Again, I could be wrong, as I've never looked that closely into the illustrator's experience).
Oh, and to answer your second question: Yes, they definitely work with the authors to remove excess description. (Or at least, they reject manuscripts that have too much in it). I've seen a lot of professional-level PB feedback that boils down to: "There's no need to say the birthday ballons are blue and red and green and the cake had pink frosting. The illustrator will decide on these sort of details and much more, so cut those lines and just keep the story moving."
(Unless the details in question are relevant to the plot e.g. it's a book about learning colors, or maybe the birthday girl hates pink and proceeds to throw a fit at the frosting color - THEN it might get left in.)
