I believe it is acceptable to write this with the adjective after the noun.
No, an adjective can go after a noun in Greek only when the verb to be is implied between them, e.g. I want clothes (that are) warm and comfortable - Θέλω ρούχα (που είναι) ζεστά και άνετα.
I'm confused about ιδιαίτερη and ιδιωτική. Are these adjectives synonymous?