Random Queries from my game today. Mostly Restaurant related.

I can't answer all your questions definitively, but I can answer the change the menu one. Click on the restaurant and go into build mode.
You will see the box in the upper left corner of the screen where it says the lot type. You at the top of that box will see what looks like gears. Click on that. You will see the option to customize menu. Click on the box with a fork and a knife. It will bring up the menu and then you click on the box with a plus sign in each category to change the options. You will have to unclick those options already chosen you don't want if it is an ea built restaurant. Then just choose those options you want. Remember there is a limit on how many items total you can have throughout the four categories.

The only way I believe you can have some control over staff is to own your own and hire the staff yourself, but I think you have limited options as there is a list of choices to choose from, but not sure 100 percent on that as I have never owned a restaurant.

I sent my sim to the library in Oasis Springs and there were skill books there, so maybe you have a glitch or a mod conflict perhaps?

If you have mcc you can change situational outfits and have it default to the category option of your choice. If you don't have mcc I don't think you can.

I hope the few I have answered helped. I hope someone else can answer the rest and if I got something wrong correct me.

Once I have visited a restaurant once, will the staff remain the same?
I'm not 100% sure on that but it does seem like the same ones working there are always there in my game.

Is there a way to maybe choose the staff?
Only if you own the restaurant. Unless there is a mod I'm unaware of.

What about delivery folks? I mean, Caleb Vatore as the grocery boy or Vlad the vendor can be kinda cute as a one off lark, but...
In my game, the grocery delivery sim is usually a teen. It doesn't matter what save I'm playing, my custom save or a premades save. As for the other delivery sims, I've only seen randomly generated sims deliver the pizza, mail, etc.

Why is there an option to "Draw on Placemat" when it clearly interferes with the meal being delivered?
To my knowledge, it didn't used to be this way. Usually the waiter would put the food on the placemat. Dine Out is pretty buggy so it may be a bug but I can't say with 100% certainty.

How do I get in to change the menus, so my awesome gallery-sourced Mexican restaurant can serve some of the great new Latin food?
@Colorist40 already answered this question, and explained it better than I can.

How come libraries don't have skill books anymore?
I can't answer this one because I usually have a rich sim buy and "donate" books to the library...if I remember to. My sims usually buy the books they need. I rarely have them visit the library.

How do you control visitors from 'out of town' (i.e. townies from other neighborhoods visiting) and Sims random outfits from festivals etc?
Without mods, I'm pretty sure you can't. MCCC can help with the situational outfits and there are a few townie overhaul mods around. I believe @83bienchen has one and also Lotharihoe as well. I can't remember which one I have and I'm not near my computer to check.

I hope some of these answers help.

Library Skill Books. You need the bookshelf from the original Willow Creek Library placed somewhere on the library premises. I usually place it in the basement underneath the library. You can either get it by going to the original library and copying it or go to the Gallery under rooms - LuthienRising Library Bookshelf.