I am hardly qualified to answer your questions but I'm sure that someone will correct me if I go way off into left field.
muminustrollus wrote:Is ginomai a deponent verb?
Yes [face=SPIonic]gi/nomai[/face] is called a "deponent" verb. This verb is either used intransitively or as a passive (with an agent) or middle. I think that in the Greek mind all "deponent" verbs are that way.
muminustrollus wrote:In that case how can it have a form both for perfect active gegona
and a form for perfect passive/middle gegenhmai? Is not just one form enough? The same seems to happen with the aorist with egenomhn and egenhqen.
[face=SPIonic]e)geno/mhn [/face] is an older form, in the NT getting replaced by [face=SPIonic]e)genh/qhn[/face].
I am not sure if this is also the case with [face=SPIonic]ge/gona [/face]and [face=SPIonic]gege/nhmai [/face] but I think it is. One form would be enough but who is going to tell them
. Languages change and here we are in the middle of a change and have ended up with two forms for the same meaning.
muminustrollus wrote:Could anyone translate these forms so that I can see the difference between them or provide meaningful examples?
I don't think there is a difference in meaning between the two aorist forms. I am not sure about the two perfect forms but I think they are pretty well identical too.
muminustrollus wrote:Another question is: why do I encounter ginomai in Mounce and gignomai in my Greek-French dictionary? Is ginomai koine Greek for gignomai?
For an explanation of Greek voice (that makes sense to me) check out http://www.ioa.com/~cwconrad/Docs/NewObsAncGrkVc.pdf
This paper is quite technical. The following one is a little shorter and a bit easier to understand.