Jm, you can begin checking in at 7 p.m. That said, people often start lining up at or before 6:30 near the churros cart on Rivers of America, so that they can choose the best seats in the front row. It is first come, first served for choosing your F! seats.
I don't know how bad the crowds will be when you will be there (early June, correct?) I saw on your dining plans that you have scheduled F! for a Monday night, so hopefully the crowds won't be too bad. However, it sounds to me like the walkways are generally VERY crowded in the early evening around NOS and Rivers, so I'm thinking it might be tough for you to check in at 7, go to DTD for a PS, and return at 8:30 for F! seating. You would probably have less than an hour for a seated dinner, and I think you might feel too rushed and stressed to enjoy it. Perhaps it would be a better night to have some counter service there in the parks, or perhaps seating at Cafe Orleans or Blue Bayou, close by? Or even, if your family is staying in the hotel and doesn't want to come into the parks before then, a relaxed room service meal?
Just a couple of ideas. We have only been there once, so I'm no expert! But we did do an early BB dinner seating (4:30 p.m.) and then the family just lounged around, shopped, did Jungle cruise, etc. while I went to check in at 6:15, and then we showed up at F! seating at 8:30. That was a nice way to do it on a VERY busy day. Spring break the crowds were so bad you couldn't really WALK along the Rivers of Am., you could only do sort of a slow penguin shuffle!