12 points? Most 12 points are used with mountaineering boots and clip in at least on the back of the boot. If they have a clip system, you will not be able to use them with most standard hiking boots.
Not quite sure about this statement. I was able to find five different brands of 12-point crampons that come with strap bindings, useful on all types of boots.
Grivel Black Diamond Petzl Stubai CAMP Just an odd comment, as I stated. I've used my strap crampons on my ski boots while in moderate terrain, mainly because they are lighter than my Sabretooths. But we're not getting into a deep conversation about 'pons here, except to emphasize that walking in crampons is indeed dangerous, not something to be taken lightly, and can lead to getting you to places off of which you may have trouble backing down. I've seen too many people crawling up and down the slope to Trail Crest to not realize that those unfamiliar with how to properly use the gear, of any type, can very easily get into troubling positions.
As for axes, there are many makes and models out there, so if you are investing, make sure you get a good all-purpose axe to start out. The length test is to hold the head of the axe, the tip of which should hit right around your ankle bone.
Again, as above, just having an axe is worthless without the skills to use it.
If you are dayhiking, you need to watch the weather reports. I just got an ultralight down sweater from Patagonia (on steepandcheap.com) and it is going to serve me very well and quite a bit this summer. You might consider (if the weather is forecast to be nice) taking a dry shirt/socks and a lighter jacket (like the Patagonia nanopuff) to change into once you reach the summit. Dry clothing can make all the difference, instead of relying on bigger, heftier jackets.
-Laura