Nope, not all of that is necessary according to everything I've found.
What I've read is 1 sq foot of space per 2 crabs, so a ten gallon set up right should hold easily 4 or 5 crabs. You can either use plexiglass to block off a water section, or you can slope the land area. Plexiglass seems to be favorite--that way they get to dig about in dry dirt rather than mud, since they like to burrow. That would require some silicone, but neither silicone nor plexiglass is expensive.
A lid of some type would be necessary--they climb. Glass would keep the humidity in better. That plus water would make getting a hygrometer unnecessary, it think--I haven't found anything that indicates they're that picky about humidity or foggers. A thermometer is good (and cheap *lol*) though they're apparently just fine in the 60's through the 80's.
Light cycle unit---er...if they mean a timer, you can usually find one fairly cheap.
Styrofoam background--not necessary. They look nice, but aren't required.
What I've found indicates dirt is preferable to sand, but the organic type potting soil (stuff without any chemicals is basically what they're saying) isn't particularly expensive.
Plants are good, but hardy plants can be found fairly inexpensively. Anubias and java fern are good, as is java moss. Driftwood would be great but is a little more pricey--maybe pick up pieces over time? Grapevine is not strictly necessary when deciding between woods, but it does look cool. A few small rocks would be appreciated as well (go to a garden center or rock store--they sell by the pound so a pound or so would be dirt cheap if you can find one that sells small amounts. I got 20 lbs of rock for less than 3 bucks).
An internal filter like
this would make a good waterfall if you wanted it--again, not a necessity and nothing I've read even mentioned having them in the tanks with the crabs, but a filter would keep the water cleaner longer. Even a DIY sponge filter would work for the amount of water that really needs to be in there.
With a little work and some creativity, it shouldn't be that expensive to set up a tank for a few crabs. Here are a few websites I found. Check them out--they're not minimal set ups, but they're not overly complex either. Good luck.
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