For red, there is some nice red jasper from Cave Creek Arizona, White I would go with howlite.

Berber agate is from Morroco.  There are several grades of lapis out there so I wouldn't rule the lapis ID out but it also could be sodalite.  I cant tell for sure from the pictures.  And I would say grossular garnets for the 3rd picture.
Don

Opal in the broadest form is just quartz with a bit of water in the atomic structure. If the water molecules line up right you get fire and if not you get common opal.  Since quartz replaces a lot of things it can be associated with organics. 

I love the 10 inch lortone saws.  I have 3 and mine have worked great.  If the saw was energized it probably was a loose wire in the front mounting that holds the feed mechanism.  Just take it off and see what loose wires there are.  You might not even need to get a new feed motor.

I have been putting together a collection of all the old magazines.  I really liked the jewelry making gems and minerals as well but they are hard to come by.  I only have a few issues in my pile.  My priority now is to finish my rock and gem collection and get all the field trip articles scanned and cataloged. I still have 15 or more years to do and 30ish issues I am missing. Then I will work on gems and minerals and lastly lapidary journal.  The 50-70s lapidary journals are really useful after they switched formats and discontinued the rock hounding trip I have no interest.  Desert magazine is another good one to get field trips from.  They are all available in pdf online.  I want to work on the mineralogical record but due to finances that one will have to wait a while.  The only other magazine I know about is there were some called Earth Science from the 50s and 60s that are pretty rare.  I only have a couple but they do have some field trips and good info.

These look more like ooids than sand grains to me.  That many perfectly rounded and sorted grains seems odd.  It can happen with ooids though and carbonate can replace to jasper/agate pretty readily.

Slabbercabber is right on on what your silicon carbide wheels probably were.  I used to use them when I started cabbing but I transitioned to diamond.  My normal set up on my loritone unit similar to yours is 120 and 220 diamond wheels for shaping, 220 and then 600 silicon carbide belts on an expando drum, and then 1200 diamond nova wheel followed by a cerium oxide polish.  Everyone has their own method but this is what works for me.

It has been 15 years or so since I was last down there but there are tons of thunderegg beds and I highly doubt all of them are worked out.  I usually would just wander around until I found someones old hole and expand it.  I am not really a fan of the geodes but my dad and I did alright the last time we went.  I would just give yourself plenty of time to explore.

I generally leave the vugs in my stones but only if it enhances the stone.  Some stones I will seal them when there is stability issues, but only if there are not a lot of them.  Other than that the cab usually ends up in my tumbler.

Looks like petrified algae from Wyoming.

top one looks like serpentine or lizardstone from Arizona and the bottom one is a mushroom rhyolite

polshedball,
your material is not tiffany.  I have seen and cut almost all the flavors and it is nothing like anything I have cut.

Judging on the color and fracture pattern, I think it is pink quartzite.  The fractures are not what you would expect from rose quartz and the pieces appear relatively durable. 

I have had the same experience with larimar as finegemdesigns.  It holds up just long enough for me to finish a cab then fractures and I start all over.  I am not sure what direction is best for your stone but I would be very careful grinding windows into it, because the vibration may loosen fractures.

Olivine and peridot are different names for the same mineral so it shouldn't really matter.  The mineral is actually made up of foresterite and fayalite in varying proportions.