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Why leptons annihilation is not 4-particles, and it is represented in the form of two 3-particles? If the pair of an electron and a positron has formed a positronium particle, then what is virtual state before the formation of two photons? What is located on the Feynman diagram between the photons emission points by the electron and the positron? enter image description here

Why is the formation of a virtual lepton with zero mass not shown for each photon emission at above picture from https://en.wikipedia.org/wiki/Annihilation? enter image description here

Imyaf
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In fact, the first Feynman diagram in your question is the sum of two time-ordered diagrams. One in which the electron sends out a real photon and later in time meets the positron at the vertex to annihilate with it and emit another photon.
The other time ordered diagram presents a positron that first emits a photon, travels on to meet the electron, and annihilates with it at the vertex to give the other photon.
The Feynman diagram comprises both diagrams at once, in a symmetric way.

So, in fact, there are 4 particles involved. Two in each time-ordered diagram. But the process itself of course involves two particles only.

By the way, space and time can have both the axes. If space were vertical and time horizontal, you had photon scattering!

Time ordered diagram:

enter image description here

MatterGauge
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