"Секси" is a sheer calque from English. As you said it, Demonic_Duck, we kind of stole it from you))) Just took the word 'sexy' and it became 'секси'. Now, this word is used mostly by girls in school)), maybe sometimes by boys. I have never used this word in my life))).
"Сексуальный" is a neutral variant. This is proper in colloquial speech (e.g. она сексуальная, он сексуальный), and this could also be used in scientific context (например, беспорядочная сексуальная жизнь).
"Сексапильный" is more common than 'секси' and it's kind of making you sound more proper and serious, for 'секси' sounds very much a slang word (maybe from cheap tabloids).
To have a good command of Russian, of course, you will need to know all these words.
The word «сексапильность» does exist.
Technically, we don't have indeclinable adjectives. If it's indeclinable it becomes something other than adjective.
Рок-музыка is a compound word. Something like your 'airplane'. We do hyphenate all such words however, i.e. 'рок музыка' without hypen would be incorrect in Russian. So рок- is not an adjective here.
Онлайн is a calque from English again. We do have some problems as to how to use it, as it's kind of a 'suckiling' yet borrowed from English, and some people tend to use it with preposition which sounds Russian-like as in "я в онлайне", some say without preposition "встретимся онлайн". So the part of speech for онлайн is not as clear here. I think the proper way would be to leave it English as in 'online-конференция' or 'online-совещание'.