The speed is completely irrelevant.
The positron is electron's antiparticle. The positron was first introduced as an attempt to explain the Dirac equation's solutions. In the Dirac equation, when you introduce a spinor Ψ as a solution, you end up that you have 4 components. From QM you already know that spin1/2 particles have 2 component spinors. So you have to explain what would the 4 components mean.
Well the 2 of them correspond to positive energy solutions with spin up or down and the other two correspond to negative energy ones with spin up or down.
That is kind of problematic though- if you allow negative energies, then the positive energy particles would not be stable (they'd transit in negative energies). So as an interpretation to avoid that, Dirac introduced the idea of Dirac's sea. The particles you deal with (spin 1/2) are fermions, and thus they must obey the exclusive principle of Pauli. The only way to avoid transitions from positive energies (where you have electrons) to negative ones, would be by assuming that the negative energy states are all occupied by electrons with negative energy.
This would though allow the negative energy electrons to absorb a photon and jump in the positive energy region. The missing "negative energy electron" seen as a hole in the negative energy sea, can be interpreted as a positive energy particle with opposite charge to that of electron.
That was interpreted as a positron. Afterwards a transition from positive energy would be allowed to fill in that hole by emission of photons. So an electron would fall in that hole, and emit photon of the energy difference... this is the interaction e^{-}e^{+} -> γγ
In order to understand how experimentally we identify positrons to electrons, you have to see what are their differences. They are the same particle (meaning that they have the same mass, the same spin etc etc) but with different charges. So how would you distinguish between them two? By how they interact with an electromagnetic field. For example electrons inside an homogeneous magnetic field would make circles to the right (let us say) but the positrons would make circles to the left. The circles will look identical but they'd have different orientations. Thus the particles would have the same mass etc, but different charges.
It depends with what process the positron will be annihilated with the electron. For example in the system of positronium (
http://en.wikipedia.org/wiki/Positronium) you can read that it lives for 125 picoseconds (2 gamma) or 142 nanoseconds (3 gamma) under the circumstances it states.
