There's a lot that you can take from opera and apply to theatre. It can make you a more well-rounded SM. Are you an ASM or SM on your show?
Regarding some of your questions:
Post-its- it depends on what you need. If they get in the way, find a way to write your info in that works for you. I'm guessing you normally put in post-its for entrances/exits, cues to do things backstage like cue prop-handoffs, etc. If you're an ASM, I think you'll find that when backstage, ASMs in theatre don't typically run their show off of their script like you would run an opera off the score. (Speaking from my own experience). If I'm an ASM on a play, I will typically run the show off of a "run list"- and my run list looks pretty similar to a WWW.
When I am an SM, I write 1-min timings into my script. I usually wait until previews to do it, once the play has settled a bit, and then I use those timings to get a sense of whether or not a scene is running long or short. If we are running 3 min longer in the first act than usual, I can tell where it happened. Just know that a play may run long or short every night and you can't use your timings as exactly as you would in opera- they will definitely vary, and probably won't settle into a regular rhythm until after a few performances.
If you know that you need a specific timing (like how long a quickchange will take) time it out with a stopwatch when you run it in rehearsal. I like to take a stopwatch to the run list the first time we run the show all the way through and clock each entry. It gives me good sense of where everything happens in the show - but times will change with the addition of scene changes, sound cues, etc so know that it's just a jumping off point. Can be helpful to update the timings after tech.
The rubber chicken is not a standard thing in every theatre. (I'm guessing you're referring to a cast joke of sneaking a rubber chicken onstage during the show.) I've never worked on a show where this happens.
Paperwork- make what you need to run the show. A run list, a character/scene breakdown, prop preset, costume preset. Browse the
Uploaded Forms page to get a sense of what paperwork others use. If you find that you need a particular thing, then make it. Not every show needs every piece of paperwork.
Stamina- I second what Chris said about finding something you love about the show. And enjoy the people- on my current show, we're doing Secret Santas, and potluck dinners on 2-show days. Just a couple of little ways to make the experience better for everyone.
Cueing- Sometimes. Actors are generally responsible for making their own entrances. But, sometimes they will need a cue for one reason or another. This can be done with a cue light, or by an ASM.
Quiet- as quiet as you need to be. You (obviously) don't want the audience to hear you, or to be so loud that it distracts the other actors onstage. Depends on the theatre really.
Opera usually happens in a much shorter timespan and often on a bigger scale (with larger groups of performers like chorus), which necessitates a lot of pre-planning and often results in rehearsals where the director moves people around like chess pieces. In theatre, depending on the director, the process can be a lot more organic, and may change a lot more during the rehearsal process. Don't let it frustrate you. It's not uncommon to do a scene one way on Tuesday and on Thursday change it completely.
Find the ways you can take the skills you already have from opera and make them work for you in theatre. It's different in a lot of ways but most of them you'll pick up naturally as you go. Ask questions! Talk to your SM. Use your opera experience to make you a better theatre stage manager.