It's easy to become overly concerned about your chickens' health until you've been around chickens for a number of years and observed them. But you will probably know when you have a sick one.
First of all, the crop is empty first thing in the morning, so you won't be able to see or feel anything. After they eat, the crop will appear as a tennis ball protrusion on the right side of the chicken's front, (like the right side of your chest). Some chickens are petite eaters and it's hard to feel, but others like to pig out, and you can actually see the bulge, as well as feel it. It should feel solid, not squishy or hard.
Regarding the pulsating throat, in some breeds, the respirations are real visible but it's just normal breathing. A lot of people mistake chicks' breathing as being labored because their little throats will pulsate so rapidly, but it's normal. Chicken breathing is more rapid than ours.
As for poop, you're looking for trends, not one-offs, as there are many different poops according to what you've allowed your chickens to eat. But it should not trend runny. There should be nice solid poop for the most part. There are exceptions, though. I have a five-year old Sussex who has had watery squirts since she was first brought home from the feed store at three days. That's just her default setting. Solid poops for her are a real head-turner, but she's a rare case.
Just watch and observe. You're spidey sense will kick in if you've got a sick one.