Can we say "Müller hat beim Match sehr gut gespielt" in order to say "Müller played very well during the match"? Or does it HAVE to be während or im?
The conventional preposition to associate a player with a match is in. Both bei and während are intellegible, but unusual enough to make your reader go "Hmmm, does the autor mean something else beyond the standard player-A-played-match-X proposition?"
Basically, in describes someone's performance in a match as a soccer match:
In diesem Spiel erzielte Spieler A drei Tore und war wertvollster Spieler.
If we talk about something that player A did or that happened that doesn't directly involve soccer being played, other prepositions would be used:
Bei diesem Spiel verletzte sich Spieler A leicht.
Während dieses Matches kam es zu Ausschreitungen unter den Fans.
Therefore, for maximum clarity, if you talk about a footballer's performance as a football player, you should use the conventionalized preposition, and that is in.
Yes, you can say both. “beim Match“ is correct. However, I would use "Spiel" or "Länderspiel" instead of match.
Yes, we can.
But »Match« is a foreign word in German. You can use it, but generally spoken, it is better style to use German words in German sentences if they exist, and there are German translations for match in German: Spiel, Wettkampf.
Müller hat beim Spiel gut gespielt.
But now you you have repeated usage of Spiel in this sentence, which is even worse.
Müller hat beim Wettkampf gut gespielt.
But Kampf is battle, fight and now the sentence has a much more martial connotation than the English one. So, if you really have to tell where Müller was playing good, then in this sentence »Match« in fact is the best choice out of three poor possibilities.
But in most cases the context is clear. This listener might already know that Müller wasn't playing the piano in a concert, and that he neither was playing Hamlet on stage. The listener might already know that Müller is a sportsman, playing Tennis or Soccer or whatever, and when you just say
Müller hat gut gespielt.
everybody will know what Müller was playing. If you want you still can add more information:
Müller hat am Samstag gegen Schmidt gut gespielt.
Now, since the sentence is longer, you also can insert the noun Spiel, since it is far away from the verb. You can even add more stuff to make the distance longer:
Müller hat beim Spiel am Samstag in der Bad Altenmarkter Scheuerstein-Arena gegen Schmidt wirklich sehr gut gespielt.
beim vs. während
Note, that beim is a contraction of bei + dem, so
- You can use it only for masculine and neuter nouns (der Kampf → beim Kampf; das Spiel → beim Spiel, but die Kür → bei der Kür)
- You can use it only in singular (das Spiel → beim Spiel, but die Spiele → bei den Spielen)
- You need dative case for the noun which can be different from nominative case (das Herz → beim Herzen, der Grieche → beim Griechen)
If you use während, you have to add an article (beim already contains an article), and you have to use genitive case:
Müller hat während des Matches gut gespielt.
Müller hat während des Spiels gut gespielt.
Müller hat während des Wettkampfs gut gespielt.
But almost every construction that uses genitive case sounds a little bit adorned, so I would avoid it when talking about sports.
Note, that in some regions you might also hear während + dative case in colloquial speech (»Müller hat während dem Match gut gespielt«). But this is not standard German. You should be able to understand this construction when you hear it, but you better shouldn't actively use it.