They're closely related. "Swag box" is a common name; "Promo Pack" or "custom promotional kit" is a more formal program concept.
Often yes, because you're coordinating:
Yes—this is a common use case. The main requirement is a clean address list and enough lead time for production + assembly.
Yes. If you do tiers, make sure your address list (or recipient list) includes a kit tier field and unit counts.
Typically:
Use:
Sometimes. The feasibility depends on:
If you're close to deadline, share your in-hands date early.