Antes de salir, mi madre tiene que dar de comer al gato.

Because Spanish normally uses antes de + infinitive to mean before doing something.

So:

• antes de salir = before leaving / before going out

You cannot normally say antes salir.

After a preposition like de, Spanish uses the infinitive.

So:

• antes de salir = before leaving

Not:

• antes de sale
• antes de salga

If Spanish uses antes de que, then you need a conjugated verb, usually in the subjunctive:

• antes de que salga = before he/she leaves

It can mean either, because salir can mean both to leave and to go out. The exact meaning depends on context.

In this sentence, the most natural reading is probably before leaving the house, but before going out is also possible.

Normally, it is understood to be the same person as the subject of the main clause, so here it most naturally means:

• Before my mother leaves, she has to feed the cat.

If the person is different, Spanish often makes that clearer with antes de que + subjunctive:

• Antes de que yo salga... = Before I leave...

Tener que + infinitive means to have to + verb.

So:

• mi madre tiene que dar... = my mother has to give...

It expresses obligation or necessity.

Because comer means to eat, while dar de comer a alguien means to feed someone or, more literally, to give someone something to eat.

So:

• comer = to eat
• dar de comer al gato = to feed the cat

If you said just comer, your mother would be the one eating, not the cat.

It is part of a fixed expression.

Literally, dar de comer is something like to give to eat, but in natural English it means to feed.

A very similar expression is:

• dar de beber = to give something to drink

So this pattern is common in Spanish.

Because a + el contracts to al.

Here, el gato is introduced by a because in dar de comer a alguien, the animal or person being fed is treated as the recipient of the action.

So:

• a el gato → al gato

You cannot keep them separate here.

In this structure, it is best understood as the recipient, so learners often treat it like an indirect object:

• dar de comer a alguien = to give food to someone / to feed someone

That helps explain why Spanish uses a here, even though English simply says feed the cat.

Yes. That is very common and very natural.

• dar de comer al gato
• darle de comer al gato

Both are used. The le refers to al gato. Spanish often includes this kind of pronoun even when the noun is also stated.

Because Antes de salir is an introductory time phrase placed at the beginning of the sentence.

So the comma helps separate that opening phrase from the main clause:

• Antes de salir, mi madre tiene que dar de comer al gato.

You could also put the time phrase at the end:

• Mi madre tiene que dar de comer al gato antes de salir.

That version usually does not need a comma.

Yes, but the nuance is slightly different.

• tiene que = has to, very common for obligation or necessity
• debe = must / should / ought to, depending on context

In everyday speech, tener que is often the most neutral and common way to express have to.

Because comer is not being used here as a noun like the eating. It is part of the verbal expression dar de comer.

So Spanish does not say:

• dar del comer

It simply says:

• dar de comer

as a fixed structure meaning to feed.