Hi FeelLion! I'm sorry it took me a while to get back to you on those pictures you posted. We've all been busy jumping from forum to forum as we try to squeeze in those last few minutes on The Forum. But I did remember to take a look at them and have a couple of ideas;
The one you have marked as Jade; Jade is possible, it is difficult to tell without a closer look at the grain structure. The other possibility, judging from the color and the way it polished is a light-green colored quartzite. If you can look at it and see that it's made up of lots of small grains compressed together, it's probably quartzite - if it looks more like a smooth, non-grainy piece, it's probably jade.
I'm pretty sure you are right on the white quartz. But a good way to double check is to take a knife with a sharp point and try to scratch it (medium-light pressure is all it takes, don't strike it, just drag the knife across the surface). If it scratches easily, it is not quartz, if it doesn't scratch or only barely scratches, it IS quartz. (You see, quartz is harder than the steel.)
The "yellow quartz" is also probably right. Though I think a slightly more correct term might be yellow jasper. This is where things get tricky; quartz, jasper, agate, chalcedony and of course amethyst, citrine, smoky quartz, and rose quartz. Opal is also related to quartz, as is girasol and several other stones. In general terms a stone's property of translucence seems to be the best way to say whether a stone is "jasper" or "agate"; if a colored quartz-type stone is pretty opaque and mostly a single color, it would be considered jasper - if it is more translucent (ie, some light can pass through smallish pieces) or even semi-transparent, and especially if it has banding or globules of colored spots, it would be an agate. But with all jaspers and agates, they will be as hard as quartz and you won't be able to easily scratch them with a knife point.
In the "unnamed 5a" picture; the whiter stone is almost certainly a tumbled piece of quartz crystal - you can see the transparent areas separated by cloudy areas which is very typical of massed pieces of quartz crystal (where they've been broken up in the extraction process or just weren't good individual crystals to start with). The other two in the top row appear to be agates, though I can't tell a specific variety. The brownish one in the lower left appears to also be an agate. The green one looks like quartzite - you can see how the individual grains show up in that piece. That is the kind of graining you want to look for in that pale greenish-white piece you have.
The photo 6a & 6b also would be agates and/or jaspers.
A few more words about agates and jaspers: Jaspers tend to be mostly in the red-brown-orange-yellow color range, though they can have inclusions of other colors, but these are the most common colors. Also, a given piece of jasper is usually one color or might fade from one color to a similar color (such as red to brown, or orange to yellow), but probably won't have definitive banding. Agates can be in almost any color, ranging from blue, red, brown, white, yellow, green, gray, to almost black. And agates frequently have bands or spots of several colors in one stone, and the banding will be well defined, it won't just fade from one color to another.
As for the esoteric/psychic properties of these stones, you'll find that agates and jaspers will have a lot of similar properties because they are all quartz based stones. They'll actually share some properties with quartz. But quartz crystals, or tumbled clear quartz raises those properties to a much higher level. The properties of an agate or jasper depend a great deal on their color or mix of colors, much in the same way that colored quartz crystals (amethyst, citrine for example) have properties that vary from clear crystal.