Earthquakes can happen when tectonic plates *move* — it doesn’t necessarily have to be the plates “pressing against each other.” It can be the plates moving away from each other. It can be the plates sliding against each other, or it can be the plates running headfirst into each other.
A *fault* results from the latter two scenarios (sliding or collision). A *rift* results from the first scenario — two tectonic plates moving away from each other.
A *fissure* is just a crack and is typically much more localized than a fault or rift. It *can* happen because of tectonic plate movement and earthquakes, but it also can have *other* causes, such as volcanic pressure or receding ground water or human drilling.
Yes, in fact, this is how we figured out plate tectonics were a thing. A scientist during WWII was using supply ships to scan the bottom of the Atlantic and found the mid Atlantic ridge. They were scoffed at, then later after the war it was confirmed. The mid atlantic ridge is, I believe, the longest fissure in the world, but it is far from the only one. In fact another major one is responsible for us in existing, in Ethiopia and Kenya. The East African rift valley is thought to be where homosapiens first originated, and will eventually form a new sea. There’s also a lot of tectonic activity there in the form of geysers and near surface magma, forming some truly spectacular and dangerous areas, in the form of lakes that will kill you almost instantly if you enter them…or even go near them sometimes because of gases.
The earth quake happens when the pressure between to tectonic plates becomes to great and it is released suddenly one plate is subducted the other is abducted. The fissures can and are (technically) a very long way away from where the tectonic plate moved.
We live in a 3 dimensional world and the shift in the plate happens under our feet, a very long distance under our feet. The average depth is 10 kilometers or 6 miles.
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