Is this correct:

Are you busy - Meşgul müsün?

Why isn´t with vowel harmony Meşgul musun?

Because last letter is l, so its hard to say meşgul musun, it should be meşgul müsün.

or for example hayal, its much easier to say hayalim than hayalım

The actual reason is historical: they are (Arabic) loanwords. There is no problem in placing l and ı in a row, it happens all the time.

because its a loanword from arabic

e.g

1. kabulüm arabic loanword 

2. golüm english loanword