Learn Portuguese (Portugal): Corte a carne e o pão, por favor.

Corte is the formal command (imperative) form of cortar (to cut) for você. To give a formal command with an -ar verb, you drop the -ar and add an -e.

Does this sentence explicitly say who is supposed to cut the meat?

No, the word você is left out, which is the standard way to give commands. The ending of the verb (corte) already tells us that the speaker is addressing one person formally.

How would this sentence change if I were asking a group of people to cut the meat and bread?

You would use the vocês command form. For -ar verbs, you simply add an -m to the você form. The verb becomes cortem, making the sentence: Cortem a carne e o pão, por favor.

The word carne ends in -e. Is there a rule to know it is feminine?

Words ending in -e can be either masculine or feminine in Portuguese, so you often just have to memorize their gender. In this sentence, the feminine word for "the" (a) right before carne is your clue.