English interrogative sentences normally begin with a verb as well: "Am I the big fish?" However this kind of sentence is a declarative question, used to express surprise or to ask for confirmation. This exists both in English and in German. https://en.wikipedia.org/wiki/Declarative_question#Intonation_and_punctuation
@razvanremo : This is weak inflection because of the presence of a definite article (der). That, coupled with the nominative case + Fisch is masculine (der Fisch) you get the 'der große Fisch'.
Alternatively you could look at it this way: since the -r is present in the definite article (der) you do not need another -r on the end of the adjective. See this link: https://en.wikipedia.org/wiki/German_adjectives
I could see this sentence being used. Say a successful businessman moves from a big city to a small town
"You moved from the city to this small town - You're now a big fish in a small pond instead of a small fish in a big pond" "I am the big fish?"
Okay this conversation would probably only happen with someone who speaks poor English but still, it could happen :D
Yes. To decline "großer" to include case and gender is called strong declension. In this sentence, case and gender are encoded in the definite article "der", and because of this, the adjective "groß" is weakly declined. Don't worry about this being too hard! If there's an indefinite article ("ein") then adjectives used mixed declension.
I've always tended to just make up my adjective endings, to the momentary confusion of German speakers who have mild difficulty understanding me until they realize what I'm doing. But I've been practicing again lately on Duolingo and although it's tough, I suggest practicing whenever you can in written German, because you'll eventually assimilate the knowledge. If you have to speak German (and therefore can't take the time to think about it mid-sentence), just relax. Your practice will eventually pay off. :)
The point is that you put in the effort and it becomes natural, and that you shouldn't let it stop you mid-sentence.. Trust me, I didn't want to learn it either (and this was after three years of German in college) but at a certain point it's essential information that you'll need to either understand or be able to impart.