Sorry for the abbreviated response I'm going to give here.
I didn't spend a lot of time in civil life. I saw no large businesses. I saw these in KRG Iraq (even big dealerships, like for farm equipment) but not in Rojava. Basically all the businesses I noticed in urban areas were what I describe as roughly family-unit sized operations run in your typical middle eastern stall. Perhaps a hardware store or something was a bit larger. The biggest 'business' I saw was vehicle repair shop with 4 or 5 stations and that was run by YPG. In civil city such a repair shop would basically be a single booth with the storage-shed style big room and they probably worked on the car while it was outside. I never saw something large-businesses esque like the kind of supermarkets you may see deep in latin America. I also did not notice much presence of 'government operated' retail business and if that was happening for anything other than bread, it was invisible to me (PYD/YPG does run some co-ops, like agriculture and textiles related stuff).
I have no idea how the farms were run. It's possible these were run by the state. The farmers are very dedicated, they gave no fuck and just kept going while active shelling/fighting was happening proximally. It is possible as I mentioned above to get bread for free in the cities. You just walk up and ask for it (of course, you could ask practically anyone for food anywhere, they would probably give you some). No money was seen changing hands, but that is at specific stalls. I do think whatever their food distribution system is, it seemed to be working better than in ISIL controlled territory -- when we took over one village people were begging in a desperate way and fighting over the little food our people were able to give. I never saw such desperation in Rojava proper (lots of beggars in Rojava, but for money not food).
Overall I did not find many devout followers of some particular brand of political writings, although I'm sure some politicians are, but I'm not much a politician myself :) A few 'Westerners' joined the Kurds with extreme political views, but anecdotally I found those people were not very well liked. I have my doubts whether the average people even give a fuck about whatever the PYD or people in charge think. The Kurds have a long history and most of that doesn't include Apo's (Ocalan's) brand of socialism, although they would surely view him highly charitably. There may be significantly different opinions in (the tip of) Northern Iraq where the hardcore socialist elements hold more sway. Then again, given the temperament of the Kurdish people I think it would be hard to impose any sort of anything on them.
I would wager as long as you don't perform some egregious crime you could get away with a lot in Rojava without the government imposing their will on you. I visited a prison and some petty criminals escaped as I was there, the reaction of the guards was just kind of 'meh' as they got away. I do not think the government has the strength to fight their existential threats while simultaneously enforcing any strong form of socialism on the populace, although doing so on a large business would be easy enough as they'd be a big centralized target.
The main attractions I would describe to Rojava are pretty extreme freedom (minimal government, you can have guns, you seem to be able to run a business pretty openly without much fanfare, by middle east standards extremely liberal view on religion, booze is sold openly, people are open and friendly and helpful, personal rights like privacy and ownership appear to be well respected, etc). If I were looking for a socialist utopia, or anything near approximating it, I would not go there.
If I could describe Kurds, I'd call them Americans of the middle east. Instead of America's de facto religion of Christianity, their 'religion' is Apo (Ocalan, the socialist). But like America, the average person seems to be not much a practitioner and Apo is more of a symbol like the cross so many people hang as much for cultural reasons as anything else. Nevertheless their culture is incredibly hospitable, so perhaps their brand of socialism can better described as just being a good neighbor and not the government putting a foot up your ass to redistribute your wealth.