No. Parks have no apparent impact on generic industry from my testing.
What I did was placed 2 little isolated groups of industry along the same road, and placed an absurd amount of parks near one group of them. Both groups upgraded more based on OTHER available services...most notably when I placed a rail station right next to them (they LOVE that).
Just placing parks didn't seen to change one group from the other group. Side note: I know offices, however, care about land value and parks can raise that.
I know that parks give little happy icons when you put them near industrial areas and incinerators give the sad faces (tying into your 2nd question), but unless there is some hidden metric that is telling one sim to go work at the "nicer" industrial building (or perhaps affecting health), they have no impact on actual performance.
I haven't found any (official) evidence to prove my hypothesis following now, so be aware that it might be wrong.
You say that you have no industrial zones at all. So, let's check this chart first:
You see that there's a production chain which requires specialized and generic industry to create goods for your commercial buildings. If you had that, you could easily lower the import rate. However, you don't have those buildings or zones so basically you import everything. You can read here too that offices are a clean alternative to industry, nevertheless they don't produce any goods.
- First off, there could be an unknown import cap. Really unlikely, but possible.
- As stated here, import trucks, ships or trains don't use the nearest entrance to your city. They spawn wherever they want to. So some trucks could be already on their way, however, they're taking ages since they have to drive through your whole city. That, too, would explain why some ships just have cargo of 50%. Maybe there are still boats on the sea coming from the bottom end of your map to your upper end. In the meanwhile, other ships spawned recognized that they don't need 100% cargo because other ships already have the cargo.
- Also, do your commercial buildings import at all? Stated here again, some buildings not connected to any industrial area nearby do most likely not import stuff.
I guess the whole problem is that you miss industrial areas. Your problem isn't well documented nor reported because it doesn't occur that often. Most cities have industrial areas, you and few others don't have them and are suddenly facing the problems of too less goods. As you can also see here, offices have some downsides:
- Fewer jobs.
- No goods.
- Less commercial tax income.
As a fellow city builder, I can just recommend you to build up some industry. The flow will be way better and less troublesome. Yes, you have pollution. Just be a dirty (real life) mayor and hide anything negative from your citizens by placing it far away from them and covering it up.
As said in the beginning, I don't have any official evidence supporting my hypothesis, but I hope I could still help you with it.
Best Answer
According to this thread you can absolutely play without building industrial zones. I think the key to it is as stated (bold is my emphasis):
You'll just have to make up for any of the industrial demand elsewhere basically.
Someone else commented:
So it seems you can either opt out of it and try to import to meet any demand, or there may just be minimal demand. If your sims are educated and there are less of a workforce for industrial jobs those buildings will be abandoned but that won't necessarily stop your city from growing.