"My golden shoes"
Translation:Mina gyllene skor
That's right. It's invariable with regards to both gender and number.
"På ett gyllene bord i en gyllene sal ligger sju gyllene äpplen"
"On a golden table in a golden hall there are seven golden apples"
No, very few behave like this. I can only think of bra and gyllene right now, but I'm guessing there could be a few more perhaps.