cities-skylines
I seem to have a lot of abandoned buildings, I'm working on why but they still seem to be around.
Do abandoned buildings sort themselves out eventually if you just leave them or do I have to demolish them in order for new buildings to build in their place?
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.
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:
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
If there is a need for the zone type, yes, abandoned buildings will eventually sort themselves out. If, for example, a high-density residential building becomes abandoned, the lot is free for new high-density residential development. However buildings that replace an abandoned one will start fresh at base level and need to work its way back up over time. Effectively no different than had you bulldozed it.
There is a downside to leaving them to sort themselves out - an abandoned building reduces the happiness values around it, has increased crime rate, and is a higher fire hazard. All of which can conspire to reduce the property values of the land they occupy and the surrounding area. This makes the land less desirable to develop, and can potentially cause surrounding areas to themselves become abandoned.
So it is typically the superior choice to manually bulldoze abandoned buildings than letting them sort out their own problems. If you are not terribly concerned about achievements, there are mods available on the Steam Workshop that will automatically bulldoze buildings that become abandoned or burn down. This can be a significant time saver when your city gets sufficiently large.