Learn Spanish (Latin America): Es injusto que tú compres la comida.

Compres is the present subjunctive form of comprar. We use the subjunctive here because Es injusto que (It is unfair that) expresses a judgment or emotion. When you state an opinion or feeling about an action someone else is doing, the verb that follows must be in the subjunctive.

What happens if I drop the que tú and just say Es injusto comprar la comida?

That is a perfectly valid sentence, but it changes the meaning to 'It is unfair to buy the food' (speaking generally, about anyone). Because you want to specify exactly who is doing the buying in this sentence, you must use que followed by the conjugated subjunctive verb (compres).

Do I really need the tú here? Doesn't compres already mean 'you buy'?

You do not strictly need it! Es injusto que compres la comida is perfectly correct on its own. Adding tú just provides emphasis, similar to stressing the word in English: 'It is unfair that you are the one buying the food.'

Why does an -ar verb like comprar take an -er/-ir ending (-es) here?