One thing I read about the Ice Resin brand is a recommendation to let it rest for 5 min after stirring for a total of 3 min (in two cups--not waxed cups of course).
Dipping the beads in resin and getting them "wet" all around before adding to your bezels should help prevent all the tiny bubbles that would otherwise get caught between them.
And btw, it's the CO2 from match flames and hair dryers, etc, that pops the bubbles, not the heat. So one good method is to breathe out through a straw directly over any bubbles which will direct CO2 where you want it.
You could try another resin but Ice Resin is one of the ones that domes. That comes with some problems though compared to "regular" resins (including that it must be sealed with polyurethane/etc) so you might want to switch to one of those if the warming, low humidity, thorough mixing (not nec. slowly), no wax on cups, dipping, resting, and CO2 don't work. For small items a longer-setting epoxy resin can even work (like Devcon 2 Ton, 30 min Set).
As I said though it's quite possible that the resin may have been too old for good performance too. Shelf life is only 6-12 months, but according to others it's a lot longer if kept in good conditions.
Yellowness in epoxy resin can be caused by too much UV light (sunglight, fluorescent light) or heat (room temperature or other heat) over time, or by creating epoxy resin items deeper/thicker than 1/2" or even less (unless that depth/thickness is created 1/8" at a time).
So either keep your items away from those situations or don't make thick items with one pour. Or you can coat them once hardened with one of the (clear, gloss) polyurethanes that have UV protection. Varathane is one brand of polyurethane that has UV protection (the water-based one at least), but that should be written on the front of the can at the hardware store. Using a coat of polyurethane will give an even tougher surface on resin items as well.
Actually, re-reading your post I see you said you purchased a medium-sized *bottle* of Envirotex Light. Assuming that was just a typo since epoxy resins (and polyester resins too) come only in two parts--two bottles, part A and part B. They won't harden till mixed together.
It also sounds like perhaps the yellowing was in *one of the bottles* however (the one with the "hardener" I guess you meant, or part B). If that's the case, it could also be excess UV light or heat (or age). If you haven't kept your bottles away from heat and light during the month you've owned them, you could probably just take them back to the store for a refund and assume that the resin was already "too old" on the shelves (resins do have a shelf life--about one year).
A hemisphere mold could be made from various materials (some of which might require a release), but a fully spherical "mold" could only be made from something like latex rubber, or several-step rubber processes.
Check out some of these links for hemisphere molds (sometimes called "ball" molds because they can be used to make 2 halves for balls), or they may be called 2-part molds or split molds:
There are different kinds of resin, and the 2 main kinds are intended either for deep molds or for shallow molds and coatings. And one "tweaked" epoxy resin (Easy Cast) can be used for both but has some disadvantages after curing.
I don't know why you're getting "bits" on your resin, but here are some other things to consider:
...basements are often damp, and humidity level does matter when curing resins
...your plastic cup may not be large enough to allow enough air to assist with the curing process, or it may keep the temp in a not-good range, etc
..."checking on it" even once or twice could allow bits to be swirled in under the covering
...your paper on the bottom of the resin may contain moisture which could cause bubbling in the resin, especially if it's not sealed... even if it's totally dry or sealed, why wouldn't you "embed" the paper in the resin rather than just pouring the resin on top of it...that would encase the paper fully, and it's even possible I guess that the exposed paper is losing bits that end up in the air??
...not sure why/how you're "soaking the resin off the pendant"...or what the "pendant" part is
...the type and brand of resin you're using could be making a difference
As I said, cured resin is difficult to sand down (you'd often need more than sandpaper for some sanding chores), and it's also difficult to do that in just one area so you can polish or coat it back to fully glossiness. You can get info on doing it though here: https://www.google.com/search?q=how+to+sand+resin
Some things will be made from materials that can shed little bits which can get onto the resin.
Are you covering the entire mold and resin, or just covering the resin areas?
When are you covering?...right away, or later?
What kind of area are you using for curing?...and area with lots of dust or lots of air circulation?
Try covering the mold with something larger than it is (width, length, height), like a Tupperware bottom or large cardboard box, or even a dome of aluminum foil. Do that right away, and preferably in a room that isn't in a drafty or dusty place (and where the temp is in the right range for curing resin).
(To remove any dust or other particles, you'd need to sand down far enough to remove them, then polish the resin and/or coat it with clear polyurethane or a coat of epoxy resin. Sanding cured resin isn't easy though. If you just added a coat of polyurethane or epoxy resin over your original resin-with-particles, they'd still show up.)
You can use any material under/inside polymer clay that can take the low heat necessary for curing polymer clay (around 275 F). Those armatures inside the clay will also be insulated from direct heat and so not get too hot as easily as the clay outside.
Air-dry clays and papier mache, etc, are commonly used as permanent armatures under polymer clay, but not sure how much "stone" or other kinds of filler Stonex has in it, etc, and stone might expand or contract a bit during heating/cooling and cause cracking in a polymer clay covering. (You won't heating the air-dry or polymer clays or the armatures to really high temps by kiln-firing, so no worries there.)
First, the brand of liquid polymer clay made by the manufacturers of Fimo (Fimo Liquid Decorating Gel, or Deko Gel, etc) has been discontinued. You may see old stock of it here and there, but generally it won't be available. There are two other brands of liquid polymer clay still available though, the Sculpey one and the Kato one (which is clearer, thinner, more heat-resistant, etc). All brands of liquid polymer clay can be mixed with all brands and lines of polymer clay though, and all brands/lines of solid polymer clay can also be mixed together (resulting in a new mix with characteristics proportional to the amount of each clay used).
You can read a lot of good info about liquid polymer clays, get lessons for using it, the various brands, etc, on this page at my site (but I haven't kept the site up for a few years so some things may be different, links broken, etc): http://glassattic.com/polymer/LiquidSculpey.htm
And if you're a newbie, you might be interested in other aspects/lessons/etc re polymer clay too. You can check out all the polymer clay topics covered at my site from the Table of Contents page: http://glassattic.com/polymer/contents.htm