Is it allowed if we make some sort of php rotation script like say we want to paste all our afiiliates in a list and it'll randomly choose 1 to display everytime a user visits the page?
Yes, you are allowed. You need to use the keyword search tools under each advertiser in order to be able to use direct links. I copy and paste their banners and then use those links in order to do it. On top, I use MaxMediaManager to manage all my ads, it works quite well.