In this sentence the ending of blauen is completely unrelated to the word Mädchen: the -en ending is here because the adjective agrees in case with the word Fisch:
der blaue Fisch (nominative) - den blauen Fisch (accusative)
Perhaps you're confusing it with the -en ending the verb (which is isst here) would indeed take if Mädchen was plural:
Das Mädchen isst den blauen Fisch (the girl eats the blue fish)
Die Mädchen essen den blauen Fisch (the girls eat the blue fish)
Many and yes.
You'll learn about the other forms as you go through the tree, but you can have a look at all of them on wikipedia (https://en.wikipedia.org/wiki/German_declension#Adjectives). Four factors influence the specific form an adjective takes: gender, number, case and the presence of a determiner (like an article, a demonstrative or a possessive). It's a lot to take in all at once, but it'll be easy if you learn and consolidate them one by one (also keep in mind that while looking at the table or at this description might be overwhelming, there is actually a very limited amount of different endings overall—namely 5—and the weak declension only uses 2).
If you have a definite article before the adjective, like in this case, the adjective will follow the ‘weak declension’ and the ending for both genitive and dative (independent of number or gender) will always be ‘-en’. If you have no determiner at all, then the endings are basically the same as the ones you've learnt for ‘der, die, das’ (see the strong declension table in the linked page). If you have ‘ein’, ‘kein’ or a possessive in the noun phrase, then the adjective will follow what is sometimes called ‘mixed inflection’, that is: strong inflection in masculine nominative and neuter nominative and accusative and weak in all other cases (you'll notice the cases where the strong declension is used are those where the determiner would have no ending).
First, das Mädchen has the defined article neuter singular nominativ "das". This clearly shows its not plural, the "das" can only be neuter singular nominativ.
Second, blauen is an adjective to Fisch. It is has no meaning for "das Mädchen" at all. Adjectives agree with the corresponding noun, so even when technically blauen could describe plural nominative with a defined article in front, it does not in this case. The noun is Fisch. Fisch is always a singular form, so blauen has to be singular too.