Use of "promise", "guarantee", "swear" and "assure" for future and past

Yes, all of these words can be used to, as you said, "convince others that something will/did (not) happen in the future/past." These words can be used regardless of tense, either past, present, or future. The difference between them is generally in connotation, or slight differences in meaning effected by word choice.

All of these verbs are fairly strong, however, it would be more acceptable to break a promise than a guarantee. A promise means one will do his best to bring the action about, whereas a guarantee means there is no chance that it should occur or fail to occur, depending on context. Guarantee is usually used to refer to future events, though not exclusively. Swearing sometimes bears a religious or legal connotation, and assure is generally taken to be a more formal synonym for promise.

All of these are based on my American English background and usage.

While you could use any of these words regarding something that might have happened in the past or will happen in the future (or not happen, as the case may be) I would say that they are not all equally applicable to past and future.

Guarantee is much more applicable to a future event. I don't think anyone would say: "I guarantee I did not eat that cake." Promise is also future-oriented, but less decidedly so. One could swear that they will (or won't) do something in the future, or they could swear that some fact about the past is truthful. I would say that assure is time-neutral in its connotation.