In Spanish, How To Say "Remember That", "Remember Doing" and "Remember to Do"?

1) (yo) Recuerdo QUE (ella) tiene que pagar las facturas hoy.

2) (yo) Recuerdo QUE (ella) ya PAGÓ las facturas ayer.

3) Recuerdo HABER PAGADO las facturas ayer.

*"(yo) recuerdo" is a literal translation of "I remember", the expression "me acuerdo" may also be used interchangeably. Both are correct.

I don't understand the structure of sentence number 4. But based on what you wrote it would be:

4) Recuerdo PAGAR las facturas, ¡No se me olvidó pagarlas!

or

4) Me acuerdo de PAGAR las facturas, ¡No se me olvidó pagarlas!

Keep in mind that these translations are not word for word, but rather complete idiomatic translations with the corresponding changes in sentence and word structure, so don't take these word for word, especially with the words you wrote in capital letters.

Other translations for "bill" are "recibo" (masc.) and "cuenta" (fem.).

I'm a college student from Monterrey, Mexico.

Recuerdo que ella tiene que pagar las facturas hoy. (remember)

Recordé " " " " " " " ". (remembereD)

Recuerdo que ella ya pagó las facturas ayer. (remember)

Recordé " " " " " " ' . (remembereD)

Recuerdo haber pagado las facturas ayer. (remember)

Recordé " " " " " . (remembereD)

4) I WILL remember

Let's look at #4

4) It is grammatically incorrect. Está gramáticamente incorrecta.

Recuerdo pagar las facturas mañana, no se me olvidó pagarlas.

Ésta oración claramente está incorrecta.

You can say: Puedes decir:

I WILL remember to pay the bills tomorrow, I will not forget to pay them.

Recordaré pagar las cuentas/facturas mañana., no se me olvidará pagarlas.