PHP and MySQL do not directly have much control over the access methods involved. This is usually a network design issue. For web sites, SSL is the secure method of choice. It could work for you, but it really depends on how your network infrastructure is designed to determine if its a good fit for you.
As for interfacing directly with EDI, I'd presume you'd need to get the specs on how your EDI interacts with other systems (direct connect? XML?) Then build from there.
You're right, MySQL doesn't have the nifty trigger events or stored procedures that were available to Oracle. You might take a look at Postgres because from what I've read, it has a lot more features and functionality then MySQL. Otherwise, if you wish to stay with MySQL, you'd be responsible for creating code (be it PHP or something else) to handle what your trigger event would have done.