Cycle 2 weeks is possible if you dose bacteria to speed up the cycling process and provided you have enough biological media such as bacteria king and lots of live rocks for the bacteria to colonize. Even if you dose bacteria to shorten cycling period to 2 or 3 weeks, you should only start with 1 fish and slowly add 1 per 2 weeks.. but you added more than 10 fishes within 2 weeks
From your sump setup, can't see clearly what's under the filter wool.. probably not using any carbon dosing method such as Bio-spheres, Nitra guard or bio-pellets? So next question is how do you deal with nutrients export? By frequent water change?
Are you using a Weipro skimmer? It looks under-sized for your 4x2x2 tank.
My guess is your biological filter is not matured and ammonia spike is killing your fishes.
Plus you added 2 anemones to an unmatured tank.. if the anemones die and you did not remove fast enough.. you entire tank will be wiped out