To my knowledge, 在 is used for action verbs. 我吃鱼 is perfectly fine (perfectly correct, perfectly natural Chinese) for meaning either "I eat fish" or "I am eating fish: 在 is not necessary, but may be added in order to emphasize or to specify 我在吃鱼 , "I am presently eating fish," as 吃 , "eat," is an action. Mutatis mutandis for 我喝茶 : it means either "I drink tea" or "I am drinking tea," but you could say 我在喝茶 to specify the latter if you feel compelled to do so.

I see French is one of the languages you are studying; 我吃 is like "je mange:" it means both "I eat" and "I am eating" (and it is not necessary to say "je suis en train de manger" when the simple "je mange" will do - although there are times when such a construction is indeed better).

我吃鱼 means "I eat fish", this kind of expression is rarely used, it appears in situations where somebody ordered takeaways, asked you which you prefer, chicken or fish? Then you'd reply 我吃鱼（的） in the context of "I want (the one with the) fish". Otherwise, you'd always say 我在吃鱼 as "I am eating fish".