بسم الله الرحمن الرحيم
(1) The work of farming fish is lawful. You should feed them pure and clean diet. You should keep the dam or pond neat and clean in which you farm the fish. The fish which is taken out of the water live and dies later it is lawful to eat it without a doubt. The fish which dies inside the water without an external reason it is makrooh to eat it.
(2) Whosoever told it, he told wrong. There is no restriction in our Shariah. You may catch the fish any day of the week.
(3) If the fish is farmed with the intention of business then zakah shall be wajib on the value of the fish provided it reaches up to the nisab and it shall be calculated on the completion of the year as what would be the value of the fish then you should pay the fortieth part of the zakah.
(4) No special dua is narrated in this regard. You should read Ayatul Kursi for barkat in the business. And start catching the fish with Bismillah, it shall bring barkat, in-shaAllah.
Allah knows Best!
Darul Uloom Deoband