Re: After Engagement...
If you are a good muslim then you can't be alone in one room with your fiance, lunch/dinner in public places might be acceptable in some cases, but its better to have parents or other adult family members around.
Interaction through telephone and e-mail is a good idea.
Talking out of personal experience, it wasn't a good idea to meet and interact before marriage as it caused lots of problems and misunderstandings and at one stage our engagement was near an end.