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In what sense is time defined by speed? Surely it's the other way around?

Currently the second is defined by a number of oscillations of a known wavelength of radiation, which explicitly avoids any dependence on space / measurement of spatial speed.

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Isn't wavelength as such dependant on space? It all seems to come together as A is defined by B and B is defined by A.

Yes, but the standard second doesn't depend on wavelength (maybe I should have said "known energy"). You take a Caesium-133 atom, look at it's emission spectrum, isolate the ground state radiation and time a number of oscillations. Of course, the radiation has a specific wavelength/energy, but the calculation doesn't depend on it.

Once you know about time, you can start talking about distance – a meter is defined as the distance light travels in a given time. Given that the meter is defined this way, defining time in terms of speed would be a bit circular.

Ok, the time dilation makes actually sense now. So like chemical reactions depend on temperature and pressure, physical reactions (if they can be called this way) are dependant on gravity and velocity (dependance on the last I can not quite get still). By physical reactions I mean the transitions between the ground states that time is defined by.

Sure, local velocity at any rate. If someone goes past you in a rocket, you'll notice that their Caesium radiation is oscillating slower than yours, so their second will appear to take longer than yours.

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