Generally cerium oxide is used to polish agate.
Bob

The best penetrating fluid is PB Blaster, found at most auto parts suppliers.
Bob

There are two clubs near you that might be able to help you.
Nevada County Gem and Mineral Society
El Dorado County Mineral and Gem Society
Bob

I use carpet scraps for my wheels. You probably can get it from your local carpet store. It is an office carpet that is 1/4" thick, probably nylon or some such material. Cut out a disk and glue it to one of those rubber disk attachments.
Bob

The light colored mark appears to be a left over saw mark that wasn't fully sanded out of the slab. To get it removed you have to go back to the coarse sanding step and sand the whole surface down below the saw mark and then go to the finer grits, sanding and polishing, etc. Polishing on the saw mark only probably won't make it look polished but will make it more evident. I use a piece of window glass and various tumbling grits with water to "flat lap" smaller pieces when I'm making doublets and triplets but this won't work for polishing. Maybe you could use a piece of carpet on your hand drill to polish it. All of this work on the surface could result in going below the penetration depth of the blue dye and the color will be less blue.
Bob

I have used the dry sanding method on slabs, the back and front of my large cabs and the backs of most all my smaller cabs. It is very fast. One of my recent monthly columns in Rock and Gem Magazine is about using the dry sanding process. I've been using it for about 40 years.
Bob

This is my rainy day cab. It was raining a lot yesterday (YEA!) so made this one. It is Brazilian that is 3-3/4" across.
Bob

I'm a lazy tumbler! I grind with 60 grit for a month, wash the rocks, put them back into the tumbler and add rocks up to 1" of the top, add water and polish  and run it for another month sometimes 5 weeks. Unload and wash the rocks and load a new batch in. This has been my method for the last 25 years. I polish rocks for our wheel of fortune at our show. I run a 40lb and 2- 12lb tumblers 24/7.
Bob

I wrote an article that was in last November's issue of Rock and Gem in my monthly column that addresses this specific situation. I use a circle template as most people do but when I draw the circle from the template I use a black ball point pen so the line is narrow and well defined. When I'm grinding to this line I go slowly and grind up to this line but never beyond it. I always ensure that I'm grinding at a 90 degree angle to this girdle. If you grind past the line you don't have a reference to know how far beyond you have gone. I use the same pen lying on its side to draw a line halfway between the top and the bottom of the preform. As I grind the first pass I'm always looking at that line and again I never grind below it. As I make the first grind depth into the dome I ensure I have ground it the same all around. I continue grinding around the preform keeping it even all the way around. I do this to keep the symmetry balanced. Sanding and polishing after the grinding activity proceeds as usual.
Bob

I just finished this one and I'm not sure where the agate is from.
Bob
 

My thoughts were banded onyx
Bob

Looks like Mexican Flame Agate.
Bob

Your particular slab is a piranha due to the bright orange layers as well as the slab shown by Gemfeller. It comes from the state of Parana in Brazil but somehow the name got changed to piranha here in the U.S.
Bob

Classic Brazilian.
Bob

I made an 8" walnut wheel that I install on my slow turning polishing unit and I use Rapid Polish on it for the difficult-to-polish material like nephrite, lapis and most anything else that tries to undercut. I could get a fair polish on some golden picture jasper with my normal method but it took this wood wheel to finish it up. The picture jasper wasn't highly silicified so it didn't really want to polish.
Bob