London 1888, several questions

[byronbay55]

Sometimes I feel quite confident with British hallmarks, sometimes like a novice....like now.

Questions
1. What do you call this item. Vesta table box / Match box?
2. Is it made in France and imported to London or the other way around. I thought "F" was the mark for import.
3. Who is the maker (or importer) "IB"?
4. I never seen a box like this before, is it rare?
5. The creast or engraving on lid (crown) anyone who knows anything about it?

Best,
Thomas