The variation in each bead really makes it hard to spot a fake, especially since fakes got better over the years.
For silvers one might say fakes lack detail, however also some authentic silver beads lack this.
As for glass and their core: TB uses a unique core size, it´ s smaller than Pandora or others. Also that core is not glued in and it's one piece. Fake beads often have larger cores or a glued core that actually consists of two parts.
In the past as a rule you could also have said that fakes were mostly current collection beads - no older retireds. Lately there is one seller which appears under different names and sells glass fakes from older designs, i.e. old earth, caterpillar etc.
So always be careful if a seller sells very rare older beads in large quantities.
As for your quandary with the ruby rock and jade beads: I prefer the jade from the left side and the ruby rock from the right set.
But why not keep both jades? It's retired and finding a nice specimen will get harder and both of yours are very pretty.