Can't you say "to" the children?
I say no, at least for British English. You buy something for somebody. In Norwegian the phrase uses the preposition til.
And if you say: Jeg kjøpte gøye leker for barna = I bought fun toys on behalf of the children
"I bought toys to the children" sounds very weird from my perspective.
Can gøy mean also English gay (happy, content) and gay (homosexual)?
Gøy just has the meaning of fun and funny, amusing.
For homosexual the two most common colloquial terms are homo and homse.
Is gøy purely an adjective or can it be used for example in the sense of 'I'm doing this for fun' (for gøy?)?