I have upgraded my ship 4 times up to now, I am currently in the Mortok systems and am constantly attacked by pirates. Every second jump throws me into an OMGAMBUSH, and if I hang around in a system, every ~40 seconds the warp gate spits out a new batch of pirates.
This situation very much reminds of the bandits from STALKER, especially their tendency to forget to switch off their RespawnExpert5000 device.
So, is there any way that I don't know of to limit these encounters? They be getting on my nerves already.

If you tend to not carry cargo, and if there are other cargo ships nearby, you ought to be ignored.. or so I would gather. (I'm an offensive pilot/trader, so I don't mind them at all.)

I carry cargo - they're there.
I don't carry cargo - they're there.
I mean, they're easily disposed of, not big deal, but they're becoming quite a nuisance, really.
And apparently I am the UniversalTarget™ for the pirates, as i haven't seen them attacking anything else. I just happen to hang around the station, then I notice the music changing and in the contact list I get 5+ pirate ships 5-6 u. away coming straight at me.
I am afraid i got a pirate bullseye stuck on my back.
I'm really curious as to whether this is the normal behaviour of the game or not, because if this is some kind of buggy behaviour, I would very much enjoy starting it from scratch.

pirate attack frequencies are governed by a lot of things, but primarily your pilot reputation and the type of system.
look at your pilot reputation and youll probably notice that your "bounty hunter" rep is maxed out... below there, youll see text that explains that a consequence of this is more frequent pirate attacks.
additionally, if youre in a system that says "anarchy" or "rebels" youll see more pirates.
put the two together, and youre almost 100% guaranteed to be attacked in any rebel/anarchy system as soon as you warp in.

Thank you, kind Sir, for pointing that out. Indeed I haven't noticed that I maxed out the bounty hunter rep.