Connecting 7200 watt generator to fuse box
No, one outlet does the job

You're forgetting that the outlet you're talking about is 240V not 120V -- 30A * 240V is indeed 7200W, so you only need the 4 pin outlet (NEMA 14-30) and matching parts (generator-cord and inlet).

(The other outlet might be a NEMA 6-30 for 240V-only loads -- we'd have to see a photo of it to be sure.  Anyway, you don't want to use it for a house hookup because it has no neutral prong, just two hots and a ground.)