Surely 'Minä ostan kermaa ja hilloa koska minä haluan täytekakkua' should also be ok?
Yes, you can leave out or keep the 1st and 2nd person pronouns in sentences like these.
(There also should be a comma before "koska" but I don't know if Duolingo pays any attention to them or not. I hope not!)
I miss leipoa (to bake) in this sentence ^^ If I just want layered cake I could simply buy it, so 'Ostan kermaa ja hilloa, koska haluan leipoa täytekakkua' makes more sense to me