Looks like the answer to most of these is, it’s not really what they do, it’s just a stereotype fueled by selective recollection. As in, when your guy friend does a “girl” thing you don’t notice, or when a girl doesn’t do a girl thing you don’t notice. And vice-versa. And it makes sense - why would you notice unless it was something that seems alien to you? So I don’t buy into this guy/girl stuff. But I can try to explain a little of the appeal of some things to me:
I like clothes as another subset of visual presentation. I’m a designer in various…genres? (tip of tongue syndrome) So I fully admit to caring How Things Look. I can appreciate nice, well-designed clothes just like I do cool artwork or a fascinating variable-driven computer animation concept.
I go shopping a lot, and usually take my sweetie with me (luckily he doesn’t mind). I’m petite but have a big butt and thus need to try things on, so unless I’ve already tried it on in person elsewhere or it’s unavailable locally and so awesome I’m willing to risk it, I don’t buy online. Women’s sizes have no consistency (I think that’s not so much a woman thing as a marketing thing), I like fitted clothes but my weight’s been fluctuating the last few years, and importantly, women’s separates are less classical than mens and more based on trends, so regardless of whether I follow trends or not (I generally dislike the idea), if I want something but don’t buy it right away, it disappears off the face of the earth (until the next retro generation, I guess). It happens by season too, so if I don’t buy, say, boots in the fall, I’m ass-out if my existing boots wear out in early spring; they’re nowhere to be found (except for the ridiculously impractical trendy ones). I’m too busy to shop multiple days a week or anything, so I go one weekend day for multiple hours and peruse a whole shopping district, have lunch, people watch, joke around with whoever I’m with and make a fun day of it. Like a long productive urban hike.
If it’s something that needs to be done, why not have fun?
Along those lines, I also care about what cars look like. I actually don’t own one myself, but when I buy my first you can bet it won’t be ugly. Same thing, design. I don’t really care how fast it can go, though, since I don’t want to get pulled over or die crashing. Maybe I would care if I were less scared of that stuff.
When Viridiano (who burps “juevos”) puts away my clothes, things do go into the wrong drawer constantly. I think it’s cute. I mean, my system is completely intuitive to me, but I have no idea how his mind perceives it, because he always forgets. And I don’t know how to fold bras either. Or iron. 
I like jewelry I find pretty (uaually sparkly, elegant stuff). I don’t care if it’s cheap or expensive (unless I can’t afford it) or whether they’re real (although sometimes real gems look prettier) and I don’t wait for someone else to give it to me. I have some very nice pieces that go with a wide range of clothing and I wear them all the time. In fact, I rarely leave the house without some kind of jewelry on, and I rotate it on a daily basis based on what I feel like.
I don’t really get shoes/bags/hats demanding as much attention as clothes. I can appreciate a pretty shoe, but clothes have so much more…variation. And bags, unless they’re high-tech and cool, just bore me. Usually they’re hyped up by their brand, which I don’t care about. Sorry Kate Spade.
What I don’t get about gender stereotyping is why men who constantly talk about girls, who they’d like to bang, who is hot, etc, etc. are never thought of as airheaded bimbos like their female counterparts are. I’ve just never understood that.
Oh, and those who think only girls feel the need to constantly rehash people’s reactions to things, you clearly haven’t spent enough time in the pit and MPSIMS. 