How do I know if one of my saline breast implants popped? I have had them for 7 years. If it did pop, could it cause my period to not start?

Saline. When saline implants rupture the breast will immediately lose volume and flatten out. It is unlikely to directly affect your period. However any emotional stress can affect your menstrual cycle.
Probably obvious. If your saline implant were to rupture it would most likely be very obvious. The saline would leak fairly rapidly and be quickly absorbed by your body. So your breasts would rapidly become different in size and shape. And no it should not cause your period to start. We give saline to patients all of the time. It should not affect your hormones.
Becomes Obvious. When saline, as opposed to silicone gel, breast implants leak it becomes quite obvious rather quickly. Generally, the patient's breasts will decrease in size and/or the patient may feel more rippling of the breast implant. Most patients present with new onset of breast asymmetry… the leakage itself should not alter the patient's menstrual cycle; other causes for this change should be ruled out.
They Deflate. Saline implants will deflate if they are ruptured. That is one of the benefits of saline implants. If you had silicone and suspected a rupture, you would have to go for imaging.