Gate is the same as door except with the fingers splayed out more to show horizontal boards, air between the fingers. Door is with closed fingers. Two flat hands, held side by side, palms facing the body, one hand flaps open at the wrist as hinges. It's a good pantomime for door. You see the door right off in the interpreted song "Paint it Black." All interpreters show "door" the same way (poorly formed). Their doors are like cellar doors. They're all leaning at 45°. Some are even on the ground. YouTube [paint it black asl] A few seconds each video shows my point. Gate is the same idea with fingertips touching.
Spy is just being sneaky. The idea is looking at things sneakily.
None of the dictionaries show the idea how I've seen it, with the sign for "mask." None of the dictionaries show "mask" the way I've seen it for "Halloween." And none of the dictionaries show "Halloween" as I've seen it. My way is better than all of them. Their way is to show the face being covered with flat hands. Put up over the face together or pulled down together. We don't like signs that cover the face.
Here's how to do "mask" or "Halloween" the cool way: Make a "V" sign. Except, move the index finger below the second finger, that is, reverse their positions. This twists the fingers somewhat. It forms half a mask to put over one eye. Bend that at the wrist 45° and place over the eye, the forearm becomes the stick that the ball mask is attached to. If you do that with both hands then "mask" becomes more complete for "halloween." Like "raccoon." Now you're cooler, more advanced, more sophisticated than all of the online dictionaries. And that's a fact.
You can use this "mask" for spy. And poke around sneakily.
This is how the dictionaries describe showing the word "spy." They all have to do with sneakily observing.
I spy with my little eye, that is, sneakily look around all over the place.
The guy who signs the song "I spy" shows the word for spy as if he's coyly looking through a monocle. He's very good in a slippery kind of way. His style has a lot of elision and sliding. The woman is there to make him look good.