You have to realize that popular culture was very tightly controlled and restricted by the Polish communist government at this time. This photo was taken at the Jarocin festival, which was a rare chance to see many bands play that otherwise had no radio play or record contracts and often played styles of music that were viewed with great suspicion by the establishment. Recording these live performances and trading tapes was often the only way people got to hear many of these bands.
I grew up in a neighboring country during this time, but I wasn't much into the rock scene then - I was into folk music, which had a similar scene in my country - many folk artists were straight up banned by the government, so it was impossible to hear them on the radio or buy their records, but tape recordings of live performances existed and were traded among the fans. Same of my favorite music from this period only existed in this form. There were even recordings of shows that got shut down by the police mid-set.
The 80s were a period of economic stagnation in eastern Europe, resulting in a lot of pent up anger and angst in the youth, and at the same time, the establishment was slowly losing its grip on the population. As a result artists were getting increasingly bold in channeling this anger and dissatisfaction, of pushing the boundaries of what was allowed, sometimes crossing them and getting slapped down - but you never knew what could happen at a large gathering of the youth back then - taping was an important tool to document and spread this to the wider population.
Pretty sure she is on a petrol one - there is a fuel tank above the front wheel, and you can see the fuel line going into the throttle body above the single piston engine. You can also see the exhaust and muffler below and behind the piston.
Also looking into it more, I don't think the Autoped was ever offered with an electric motor. Apparently the confusion comes from the fact that the company was bought out by the battery manufacturer Eveready, and sold as Eveready Autoped. Eveready modified the Autoped by adding a battery and ignition coil, replacing the original magneto system, but propulsion was always by means of a petrol engine.
I don't think the one in the photo has the battery and coil however - the coil can be seen here in front of the gas tank, but is missing in the OP photo.
Edit: looks like the batteries and coil might have been separate - here is an article from 1917 that describes the Autoped as having a magneto ignition system (no coil) and also a battery box to operate the front and rear lights. And here is an example with an ignition coil powered from the wheel, but no battery box and no lights (which were probably optional) The one in the OP does appear to have the battery box and lights, but uses the magneto ignition, so it's the same model as described in the article.