Can I mix LOOK pedals+cleats with SPD-SL shoes?

Whilst the shoes are marketed for SPD-SL cleats because that is the Shimano system and you have Shimano shoes, this is really referring to what we call a 'three-bolt' pattern. Both SPD-SL and the look cleats are a 3 bolt pattern so the cleats are compatible with the shoes.

See how there are another two bolt holes in the middle of the three-bolt pattern - in the same manner, those are compatible with any two-bolt cleats, i.e. mountain bike cleats like Shimano SPD, but not limited to one brand of cleat.

You must use the right cleats for the pedals, which is fine because your cleats came with the pedals. Shimano ones look quite alike but aren't the same.

Cleat adapters are indeed for helping you to walk with more grip, as well as to stop the cleats from scuffing and wearing down, but the SM-SH40 are for 2-bolt mtb cleats fitted to a 'road' shoe where they are not recessed. These metal cleats are particularly slippy to walk on if exposed like that.

There is another product, removable covers for plastic 3-bolt cleats, which protect the cleat when you walk around off the bike, but you have everything you need to ride in the photo. Not a whole lot of people even own covers, sometimes I take my shoes off if I want to preserve the cleats and have to walk any distance.