Oh, is sneaking a rubber chicken onstage something people do? I thought you were talking about it being an actual prop. I'm ashamed to admit I've done a show with an actual rubber chicken... and a different show with a human dressed as a chicken... I do some very silly plays.

For cuing actors' entrances... they'll often be left to figure it out on their own, assuming that they can hear and/or see the action onstage that they take as their cue. If there are points in time where the actors backstage cannot be aware of what's happening onstage, then you'll want to have a cue light system, or else have an ASM who can cue them based on your call over headset. I work with a lot of Deaf actors so I actually do a LOT of cuing actors for entrances... probably more than is common in most theatres. But outside of that, if there are moments where you want the entrance to be based on a visual cue but the entering actor can't see it, then they will need a cue. For instance in my current show, J has to pop her head out of a door right as P approaches the door, but she's behind it and can't actually tell when he's approaching a) because she can't see it and b) she's Deaf so even if it were on a line she still wouldn't know, so we take that one off a cue light.
For paperwork, if WWW is what works for you, then run with that format. I think that makes a lot more sense than trying to teach yourself a whole new system of paperwork. You may find that you don't need quite as much information as is usually in a WWW... but you'll figure that out as it comes up.
For timing, I've only ever worked by timing complete scenes, but I'm seeing people here say they either time each individual page or they mark out in the script each time a minute passes... These are both excellent ideas and I may have to try them! Since my next show is a radio drama and is VERY time-sensitive

Things ARE often squished together in a script. I take my notes in the initial copy, but when I'm turning it into my calling script, if there's one moment that needs a lot of cues, I'll put lots of space in the text of the calling script, so that it doesn't look like I'm running my cues over into the next segment.