As best as I can tell, they mean the same thing, but fikir is definitely an Arabic word in origin, whereas düşünce is more likely a Turkish word in origin. It's pretty likely, as I know this phenomenon occurs in Arabic dialect, so it follows that it can occur the other way around.
That's my £2 on that.
Düşünce, Fikir and Görüş can often be used interchangeably, however, there are slight differences, depending on which context they are used.
As a general rule of thumb...
düşünce = thought, idea
fikir = opinion
görüş = view
bakış açısı = perspective, viewpoint, outlook
Bu çok iyi bir fikir. Sen ne düşünüyorsun? Benim görüşüm farklı.
(This is a very good idea. What do you think? My opinion is different).
düşünceleri you can take a look at this https://www.duolingo.com/skill/tr/Possessives/tips-and-notes