QcuteQcute Tactical Backpack, Waterproof Military Cross-body Molle Sling Shoulder Backpack Chest Bag for Outdoor Every Day Carry

Q: Does it have a pocket in the back where the strap at?

Yes, a large pocket but there's not much room because it's not very thick.Ight be good for a medium size laptop.

Q: Will this bag fit a full size set of hunting binoculars?

My full size iPad 8 fits in it just snug, like it was made for it. I’m not sure if the width dimensions, but my iPad 8 stands 10.2” high. It just fits length and width wise but also there is much air room on either side of the iPad with the inside pockets for me to keep my house keys, chargers, cables, etc. with room to spare.