If you choose the option "jest", you have to decline the word "zwierzę", so it would be: Ryba jest zwierzęciem (instrumental case). If you choose the option "to", you have to use nominative. Consequently, the sentence "Ryba jest zwierzę" is incorrect. You can choose both options.
How do people use these options in common speaking? i.e. which way is more formal? what should I use when I approach random Polish people?
Jest is definitely more formal 'cause it sounds more natural. "Ryba to zwierzę" means something like "Ryba = zwierzę" so it's more concrete but simpler.
The word 'to' generally means 'this' and is used for neuter nouns (to dziecko - this child, to zwierzę - this animal, to badanie - this research).
'To' is also used in two grammatical, easy construction, which you experience in the first lessons.
'To jest X...'; X being in nominative case, translated as "It is X" ie. To jest chłopiec - It's a boy; To jest dziewczynka - It's a girl.
'X to Y'; both X and Y being in nominative case, translated as "X is Y".
Hope it helps exploring the mysteries of Polish :D
If i use "to" in a phrase so it couldn't have a gender at the noun ?? Is it right ?
Sorry, I don't understand what you mean... "to" doesn't have anything to do with gender.
Drat! Pols have no articles; does it really matter if you don't put "an". Its a correct translation
It does, because you have to create a correct English sentence.
It doesn't matter if you just get the word "ryba" to translate, then you can just write "fish" without an article.
Which part? If you get a Polish sentence to translate, you have to translate it as a correct English sentence. "Fish is animal", "The fish is animal" and similar are not correct sentences.
If you translate just one word/phrase, then you can treat it as in the dictionary, so you don't have to write "an animal" nor "the animal", "animal" should be ok.