Learn German: Gib mir die Munition, ich bin am Kämpfen! - Give me the ammunition, I am fighting!

This is the colloquial am-Progressiv. Standard German does not have a dedicated continuous tense like English, but in spoken German, you can express that you are actively in the middle of doing something by using the conjugated verb sein followed by am and the infinitive of the action verb. Here, it literally translates to 'I am at the fighting.'

Why is Kämpfen capitalized in this sentence?

Because it acts as a noun in this grammatical structure. The word am is a contraction of the preposition an and the dative definite article dem. Because it follows a hidden article, the verb kämpfen becomes a nominalized infinitive. This means it is treated exactly like a noun and must be capitalized.

As a refresher, why is the command form Gib instead of Gebe?

The verb geben is a strong verb that changes its stem vowel from e to i in the informal present tense, as in du gibst. When forming the informal singular command (the imperative) for verbs with this specific vowel shift, you keep the shifted i vowel but drop the personal ending and the pronoun.

If I wanted to specify who I am fighting, could I add an object and say ich bin am Kämpfen den Feind?