Starting with the ones I don't like and why I don't like them:
01 doesn't really work as a logo, and 02 is too bold in several ways.
05 Some resemblance to the Xbox360 logo, requires two colors.
06 looks like Pandxra to me.
07 I don't think "P&|A" should be in the logo. It's too dark, and I don't like the font, particularly because the o doesn't really look like an o.
08 Too complex, too "real". Bad choice of color and font.
10 Too wide as an icon.
11 Fireworks? Too complex, too playful.
13 I just don't like it, I don't know why.
16 and 17 lack curves, the color doesn't work.
18 Don't like the font, perspective on box is wrong
19 No icon, P&|A
20 ??
21 Well done artistically, but the big checkmark makes it appear like some "healthy food" logo
22 Too "retro".
And the "good ones":
12 seems alright though retro as well, but only variants 2 and 3. Antialiasing hurts the thin lines a bit, maybe HanDuo can make it bigger.
04 and 15 look nice, but they somehow lack the symbolic meaning. In a way that is true for 09 also, but that one looks really cool.
14 works very well as an icon, just feels slightly too unexciting. I like the variant with the single leg, turning the box into "pa"
03 is quite brilliant: a very simple geometric shape that manages to encompass the box, the letter P, and the "play" symbol. It can be used as an icon and works in b/w. My favorite, but it also feels strangely familiar.