Is the shuttle allowed to clip the net on the serve? I can't find any laws regarding this (I think...). Thanks.
Yes, there is no fault like tennis for the shuttle hitting the net though if it ends up going in you'll be lucky.
Someone told someone else that the server has to have eye contact with the receiver during serving...is that correct? I've never read or heard that before
No, that is not true. You need to ensure that the server is ready but you can do that based on his stance.