Learn Polish: Nie mamy taśmy, chociaż mamy dobry klej. - We do not have tape, although we have good glue.

This sentence is a perfect refresher on the 'genitive of negation.' The verb mieć (to have) normally takes a direct object in the accusative case, which we see in the affirmative second half of the sentence (mamy dobry klej). However, whenever a verb that normally takes the accusative is negated, its object automatically switches to the genitive case, giving us nie mamy taśmy.

Since mamy takes the accusative case, shouldn't dobry klej have a different ending rather than looking exactly like its dictionary form?

It actually is in the accusative case! Klej is a masculine inanimate noun. In Polish, masculine inanimate nouns (and the adjectives describing them) have an accusative form that is exactly identical to their nominative (dictionary) form. So dobry klej is grammatically accusative here, even though the spelling hasn't changed.

Could I use choć or mimo że instead of chociaż here?

Yes, absolutely. Chociaż, choć, and mimo że all mean 'although' or 'even though' and are largely interchangeable in this context. Choć is just a shortened version of chociaż and is extremely common in casual, spoken Polish.

Is it required to repeat the verb mamy in both clauses, or could I drop the second one to sound less repetitive?