Is it possible to have an invert only tank? And how small can I get away with going for? I know they say the bigger the tank the easiest, but how big do inverts need? Are they easier to care for than fish? Are all these things compatible?
Welcome to Reef2Reef!
Yes, it is possible. The tank size depends on the specific inverts, and a lot of people will have different opinions on what size of tank you'd need.
That said, for everything you listed except the lobster (which long-term would need an enormous tank), you could probably get away with a 40 gallon breeder tank, but obviously the bigger the better, and a lot of people would likely say that's too small for the arrow crab. Regardless, since most inverts don't swim, maximizing walking and climbing space in the tank would be suggested.
For the starfish, most starfish do not do well in our tanks.
Some people report moderate levels of success (i.e. where the star lives like 2+ years) with Chocolate Chip Starfish and with
Goniaster tesselatus, but others don't have that much success with them. Very, very few people report any decent level of success with other stars like Linckias and Fromias. The only true starfish (Asteroidea) that I personally feel alright recommending for people to keep if they really want a starfish at this point are Aquilonastra stars (known in the hobby as "Asterina" stars) - they multiply fast enough to be considered pests, and some species under some circumstances may eat some corals like zoanthids, but they're cool, generally little stars. Otherwise, if it doesn't have to be a true starfish, I recommend Brittle/Serpent stars (Ophiuroidea), which typically do fine in our tanks.
The shrimp, arrow crab, and decorator crab would probably be compatible (though I'd ask if anyone has kept an arrow and decorator together before to be safe). I don't know for sure with the lobster, but I'd assume that one wouldn't be safe for the others (I haven't looked at lobster too intensively yet, but I have heard report of them eating snails, hermit crabs, and sometimes fish). Aquilonastra starfish would be fine with those, though, as would brittle stars (with the possible exception for the "Green Serpent Star,"
Ophiarachna incrassata, which is know to be predatory at least toward fish).
Some inverts (like Aquilonastra stars, a lot of snails, etc.) are easier to care for than most fish, others can be very difficult for one reason or another - regardless, a lot of inverts are much more sensitive to water quality than fish are, so good, stable water quality is important for them.
Edit: Ah, the comment below made me realize that I should point out - the inverts you mentioned wouldn't be difficult ones; just make sure you don't get copper or other toxins in the tank, maintain decent and relatively stable water quality, and they should do fine.
