Hi hi!
Home Depot or Lowe's should have regular playsand, and you can get a hygrometer from the lighting/and/or humidifyer section of the same stores. Be sure that the sub is a minimum of 6" high, ooor three time the hight of your biggest crab - whichever is deepest.
Crabs should always dig underground to moult. If you catch one moulting above ground it's called a surface moult - and you should isolate this crab as it will be vulnerable. Deep sub will help reduce risk of surface moults.
Humidity can be improved by sealing the top of the tank (what kind of lid do you have? If mesh, covering with plastic wrap or press and seal will do the trick... I have an acrylic lid, which works really well), and by adding an airstone bubbler to the pools.
Lights tend to zap humidity & arent putting out heat at night if you turn them off (which you should), so I would recommend prioritizing a heater. "Under Tank Heaters" (used on the side, not the bottom of the tank like the name suggests) are typically the best option, and a brand called Ultratherm are best for crabbers because they can be insulated if need be. But you're working on it, so that's good!
Distilled water isn't ideal - the best thing is probably to use tap water, with a dechlorinator. When you buy dechlorinator, look for three things: that it removes chloramines, ammonia, & heavy metals. It'll say it does on the lable. Prime is a popular brand.
Salt: unfortunately, All Living Things salt doesn't have the minerals and elements that the crabs need to be healthy over the long term. What you want to get instead is a synthetc Marine Salt Water (or MSW) salt, made for salt water aquariums. (And don't get 'Aquarium Salt' either... it's not the same thing... lol, so much to remember! ). Common brands include Instant Ocean, Kent Marine, and Red Sea Salt. Pet shops that sell saltwater fish will have this, and it can be ordered online.
While calcium is super important, calcium with d3 likely isn't necessary for crustaceans IMO... we don't have any evidence that d3 is useful to them (that I've ever heard of) - they aren't like vertibrates in terms of many of their bodily processes, and this isn't surprising if you consider that they evolved along very different branches from vertibrates generally, and reptiles (for which we design calcium powders) in particular.
Anyhow, sticking a cuttlebone in the sand & leaving it there offers the crabs a constant source of calcium for them to pick at & saves you having to mess with powder (I know I can't seem to touch calcium powder without getting it everywhere

). Just a thought.
Crabs do periodically become inactive, or slow down prior to a moult. Keep an eye of your lethargic crab, making sure he doesn't ditch his shell or begin moulting on the surface - but otherwise try not to worry.... their moulting cycles can dictate whether they are active or pokey. Their appetites can be affected by moult cycles too - don't worry if they don't seem to be eating.
Food:
Crabs tend to eat relatively small portions. If you cut up cooked or raw veggies & fruits & put them in freezer bags, they last a looooong time. Ditto seafood - a bag of raw shrimp and/or clam meat (check for preservatives ) lasts foooorevaaaar. Freeze dried or frozen blister packs of bloodworms, krill, mysis shrimp, clam, brine shrimp, or whatever from the petstore are great (still checking for preservatives ). I make powdered dry food mixes from anything & everything on the safe food list and feed these when I feel lazy (most of the time

). You can put organic baby food in ice cube trays & transfer this to freezer bags for quick fruit & veggie fixes.
Cut stuff up teeny: crabs have miniscule mouths.
I'll link the crab nutrition page in case you haven't seen it yet - it's super good reading. Don't underestimate the nutritional value of dried leaves & bark. Also - worm and herbivore (like rabbits or deer if you can get it) poop. If your snake isnt on any meds, it's sheds will be welcomed with open claws.
As for ALT brand... I don't pretend to know every product they offer, but they make enough crab un-safe stuff/useless junk that I wont give them my money. Honestly, their lack of research & apparent disinterest in providing good quality products for hermits makes me very annoyed. Ditto other pet companies. As much as possible, I personally avoid pet store brands & source cheeper/ better stuff from groceries stores, hardware shops, or else buy from small online crab specific retailers. But that's me. I get grumpy about this topic.
Check out the retail resources listed in the FAQ section! There's good stuff! Some of our members even have shops.
Organic *unpasteurized * honey is considered a healing food - and crabs really like it. You can offer your little guy some of this.
I think you mean "autotomy" and not "autonomy".... when legs fall off, right? Autocorrect doese not like this word. Best way to prevent any kind of illness is to provide proper temps, high humidity (80% +), lots of hiding places, deep enough substrate (crabs really need deep sub), aaand a varied diet. The rest is luck. It's probably good that you don't handle them much - this will likely help them.
Correct marine salt is also key to good health - if they have as much of the trace minerals/salts and calcium as they need, it'll go a long way to keeping them healthy. These things facilitate chemical bodily functions.
Falling from hight within their tank is unlikely to harm them. They climb a lot in the wild & presumably fall sometimes. I've read a couple instances of a fall off a table onto a hard floor causing a cracked shell - but it's really rare. I'd file this concern under "don't worry about it."
Yes a change in environment can cause stress. Providing lots of hiding places can help to minimize this.
The Shell page! It has species specific lists of prefetrred shells, as well as shells to avoid. So useful. You can find it in the FAQ ... and the shopping resources lists places to buy shells. (I'm partial to Richards, myself.)
Nutrition page:
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