uh i wrote a really long reply about water conditions in a previous post but i cant find it now... so ill make this one slightly shorter. 10 gallon is pretty small, i suggest 10 gallons per single adult. if u get larger tanks u can do maybe more axys per 10 gallons but if u want 3 axys i suggest atleast a 30g. as with everything, the bigger the better.
as for cycling, yeah its necessary, i read from some "experts " that its not necessary but they breed and sell so the axy usually doesnt spend too much time in their hands anyway. i always think u should go with the safest bet. Cycling settles a biological micro environment in ur tank. these are things like certain bacterias that will reduce ammonia levels and keep ur axy healthy. if u dont want to take a full weak cycling u could use api quick start. its suppose to have cultures of good bact already in it. idk how well it wworks, i just bought it but its an option. when ur tank is cycled and u want to clean it bc its dirty or bc of algae i suggest u take out some of the old water and substrate and keep it somewhere and add it int he new and clean tank and water after. tht will help speed the establishment of the bio-env. hope this helps