Yes to both questions. Yes, action declarations are normally visible to everyone (it represents the start of an action--more intelligent creatures have faster OODA loops (
https://en.wikipedia.org/wiki/OODA_loop) and can delay committing to an action). Yes, intelligent enemies get the same benefits as intelligent PCs.
If the players are fighting an Ogre and a Mind Flayer, the DM will say, "The Ogre smashes Ralph flat with his club--or tries to anyway. What do you do, Ralph?" Maybe Ralph declares a Dodge, so the Ogre will have disadvantage, and then Belinda declares that she's hypnotizing the Mind Flayer with her Hypnotic Gaze, and Peter says he's going to shoot the Mind Flayer full of arrows while keeping his distance from it. Then the Mind Flayer, because he's the most intelligent, gets to declare his action. The DM says, "The Mind Flayer maneuvers so that Belinda and Ralph are both in front of it and then blasts them both."
Then everybody rolls dice and resolves their actions. (It's fine if they roll dice beforehand, just as long as they don't show the results to anyone who is still declaring.) If necessary, roll initiative to see whose action happened first. E.g. if the Ogre hit Ralph but failed his save vs. Mind Blast, the Ogre and the Mind Flayer both need to roll their initiative to see if the Ogre actually got his smash in.
I would also let you convey a "fake" action using Deception, e.g. "I'm going to try to look like I'm just dodging but really I'm about to Action Surge and attack the Mind Flayer four times," which is mechanically just the regular four attacks on the Mind Flayer, but with an Deception vs. (better of Perception or Insight) contest beforehand to see if the Mind Flayer falls for the deception. And maybe I'd also impose disadvantage on any initiative checks to represent how the deception slows you down by a second or two.
It sounds like you're on the right track. Let me know how it goes for you!