Well, you've sort of got me. I agree that if you had the bar on your back as you did that motion, it would be a "wide stance, toes out" squat (I guess some people call that a "sumo squat" . . . not sure if it has any other formal or informal name(s)).
The fact that you're holding it below your body is enough to qualify it as a deadlift in my book, however . . . sort of a semi-arbitrary naming convention.
But . . . this is not to imply that the squat and DL are interchangable. They do work the body in signficantly different ways. The DL works grip and lattissimus muscles in ways that the squat does not. It also works the hamstrings and spinal erectors to a greater degree.
Squats (to me) work the quadriceps more, and the gluteus "differently" (not more or less, just "differently") than the DL.
Note also that squat comes in many, many different flavors ... bar high on the back, bar low on the back, front squats, overhead squats . . . they all work the body differently, and all are valuable.
If you like doing the move you describe, and it's not hurting you, I'm not sure that it matters too much what you call it.
About Q1: I honestly don't know. The only thing I've consistently heard about foot position is that your knees should track out directly over the feet (at whatever angle the feet are turned). I tend to have a fairly straight-ahead position (turned out only a very few degrees), but it does get more turned-out under heavy loads . . . but still probably to no more than 1 o'clock and 11 o'clock.
About Q2: Well, I think you're generally allowed to 'touch and go' . . . your DL can touch the ground, but shouldn't actually rest on it. However, I break this rule all the time, particularly in a long set where I need to re-set my grip to keep going (I have a very lousy grip; it often fails when my legs/back can keep going).
It seems to me this is a personal call, and depends on whatever standard you want to hold yourself to. Certainly if I just "touch and go" I consider it an unbroken set. If I put the weight down just long enough to re-set the grip (less than a second), I'll still call it one set. If I stand up, breathe, or walk away, well, that's not one set . .. . (unless, of course, the whole protocol is one of Pavel's "breathing ladders" or something . . .)