Running

Like the other poster said, zero drop and barefoot are different things with obviously some overlap. Personally, I don't like to call anything "barefoot" unless you have nothing on your feet (more to be precise than gatekeepy).

Running actually barefoot takes some building up to. Any time you run, forward momentum is generated by shear forces at the ground, and with a shoe on, it can be distributed throughout your shoe. Barefoot, all the shear can only go through the relatively small contact patch of your foot skin. As you can imagine, that's a recipe for blisters until you've built up strength in the skin. As the skin gets stronger, it also gets more puncture resistant. A big part of the adaptation to barefoot running is learning, too. When you run in thicker shoes, your foot can drop onto whatever surface you want, and it doesn't matter. Barefoot, you need to be lighter on your feet and more adaptable, so if you see something you don't want to step on, you can take a shorter/longer/wider step, and if you step on something sharp, you can quickly shift such that you aren't putting all of your weight onto that spot. It's hard to learn, and it requires the buildup of some of the intrinsic muscles of the foot, which are laughably underdeveloped for people who habitually wear shoes.

Minimalist shoes, on the other hand, still require some of that learning, but much less, and they don't require skin to build toughness the same way. Personally, I've found minimalist shoes to be much more durable than maximalist, largely due to the lack of high foam stacks. The breakdown of foam is what makes you have to retire a pair of shoes, usually. People who run a lot and rotate through different shoes generally get a sense of when a pair of shoes needs to be retired, though there are plenty of people who wear a pair for way too long cause they aren't visibly damaged. With minimalist shoes, you largely can just wear them until they are physically damaged too much.

Personally, I find toe shoes gimmicky, and i don't think they actually provide more flexibility or traction or anything.

Zero drop just means that the heel and ball of the foot are at the same height, so you can have a heavily cushioned shoe with zero drop. Some shoe companies cheat a little by measuring to the toe, and having the toe lifted by a bit, so you actually have a drop to the ball of the foot, but then it gets canceled out by rocker geometry.

Most shoes (running and otherwise) are designed with a drop. This means that your calf muscles get shorter. If you wear shoes without a drop, your calves will get stretched more, and in some people this manifests as calf soreness or pain or Achilles pain. This soreness/pain will be correlated with both the change in drop vs what you are used to as well as the speed you are running. For this reason, I would start zero drop running on trails, not pavement, because you will be going slower, and the varied terrain will force you into a bit of a faster cadence. I know plenty of people who wear zero drop only on trails, but not pavement. Ideally, if you go that route, aim for something with a small drop (4-5 mm) for the road shoes.

I used to run barefoot or in minimalist shoes, but as I upped the distance I was running each week, I switched back to shoes with some foam. I think the biggest thing is that I found my fit. I wore huaraches which let my feet expand to their preferred width, and now I pretty much exclusively wear Altras. The started advertising their shoes as "foot shaped" and zero drop, and their "original fit" is actually their widest, while their "signature fit" got narrower. "Lone Peak" are their highest recommended trail shoe. They do have some "short drop" shoes as well.

I think for me, one of the most important things I did was basically just eliminating all toe-squeezing shoes from my life. My running shoes don't squeeze my feet at all now, but neither do my casual footwear or boots. If you don't do that, you are giving competing stimulus to your feet.