Re: Black "Onyx."  Depending on how much you actually need, a 40 x 30 mm. cab (or smaller) from a supplier like Kingsley-North might do the job for you.  I've sliced up several for various projects over the years and they've worked just fine. 

New Era Gems used to offer slabs -- inquire, they might still have some kicking around.     

Welcome from a "neighbor" just down the coast in Camarillo.  There's much to learn here.

Seize the Carp!

To me the first one looks a lot like some of the old Owyhee Jasper.  Hard to say for sure though.

Greg, I think most of the commercial embedding is done using vacuum to pull the bubbles out.  I used to embed little turquoise chips in Epoxy 330 for certain jewelry pieces and found that gentle temporary heat makes the epoxy more liquid and allows bubbles to move to the surface and "pop."  Too much heat for too long causes the epoxy to set up, of course. 

It all depends on the size and shape of the "chips."  If they're very small but bright the best use is probably inlay or embedding in plastic.  If they're large enough to cut as cabs, orientation of the best color play to the top of the stone is the most challenging element.  Many times the color play is just on a narrow edge or is situated on a very thin part of the rough, making cabbing impossible.  Much Mexican opal is also quite unstable and is subject to crazing after cutting. 

It's hard to give advice without seeing the stones in question.  A few pictures would help.

   

It looks to me like a scrap from the trim saw that someone's tumble-polished.  I've polished a number of similar pieces.  It makes a nice conversation piece.

Welcome from southern California.

Welcome from southern California.

Welcome from southern California.  You'll have fun here.

Welcome from southern California!

There are some grades of Guatemalan jadeite that are definitely blue.  The GIA had images (which I can't locate at the moment) of pieces that were strongly blue with almost no gray.  But I agree with Isotelus that most "blue" jadeite from there is grayish-blue at best.  I went to a large exhibit of Olmec jade and other antiquities a few years ago and was disappointed not to find fine-colored blue material.  Most was a little less green that the material used in this miniature Jadeite mask I bought in Guatemala some time back. Sorry about the image size -- Photobucket wouldn't allow me to resize it tonight for some reason.

 

In the "olden days" (my time) they were called up-eyes.  You can find a wide selection of Sterling and plated types, along with bell caps, here:

 http://www.firemountaingems.com/shop/kwctfnbailhalfdrill

Larry, the harder the stone, the higher the speed.  This link gives general stone drilling instructions and has a speed guide if you scroll down.  I think they recommend 18,000 to 28,000 rpm for your size drill bits with hard stones like agate and jasper.  I also noticed drill stands are available from Dremel for its various models.

   http://www.inlandcraft.com/howto/drilling/using_diamond_drills.htm

This Dremel chuck should handle the range of shank sizes you mention:

http://www.dremel.com/en-us/Accessories/Pages/ProductDetail.aspx?pid=4486

I use bits from 1 mm. up to 5/32" with my Foredom #30 handpiece which can be converted to a drill press.  You'll need a flex-shaft motor, shaft and drill press accessory though. 

I don't know about Brazilian agate ballast being dumped but I do know that German immigrants in Brazil used it as ship ballast in the 19th century to ship to Germany to revive the agate-cutting industry in the gem center of Idar-Oberstein.  The local German agates that had supported that industry for several hundred years were depleted and  the local cutters were overjoyed to have an abundant source of new agates.  The Germans found some truly beautiful Brazilian agates that are on display in the twin cities' museums I had the good fortune to visit several years ago.  They also learned to dye grayish agates for uses as bowls and other objects. 

Here's one example I photographed, and there are many more on display: