You'll find a few specific topics that will answer some if not all of your questions here in this sub-forum.

Answering all of that in one setting is like eating a cow...

Ultimately, there's more than one way to skin a cat, and everything that works will also NOT work sometimes. Being adaptive and intuitive about your hunting, but keeping it as simple as possible is what usually ends up being productive for calling coyotes (or any game hunting really).

The best I can answer your shotgun question "how do you call coyotes?" in shorthand is this:

Keep it simple, but strategize appropriately for 'set' placement based on the terrain and animal pattern in THAT specific area (See thread for set design).

Read the wind and LIVE BY IT.

Don't move on stand.

Prey distress sounds work almost all year, other sounds work well during certain times too (see thread for "year round call sounds").

Vary your calling sequence according to YOUR specific area/terrain, interest level, time of year, and hunting strategy. Usually less is more.

Wear camo that matches YOUR specific surroundings at that given time of year.

Calling from the ground is most common and most productive, but blind or stand calling can be effective also.

Not a lot of help, I know, but hang around long enough and you'll notice I have a bad habit of writing books on here, which I'm trying to break. Ask specific questions, get specific answers.