Your limitation will be the 12V port. Ownership said it could handle up to 15A/180W but fortunately also included the relevant manual page, which clearly sez the 15A/180W is peak only. Iirc, 11A and 160W were the continuous numbers. Anyway, it's in the manual.
Would recommend a 12V adapter for your laptop. Got one for a MacBook Pro via Amazon and it works great. Less loss, too.
So that leaves the air mattress pump. Check the specs for a 400W and 800W inverter. A 400W will probably work fine.