1.
In Adobe InDesign, there's a Glyph Panel that allows you to view all the glyphs in a font, and insert ay glyph into your text. Prior to InDesign CS3, the glyphs were displayed in the same physical order they happen to be stored in the font (GID/CID order). In InDesign CS3 and later, the default is to display them in Unicode order, though one can optionally change to Unicode order. Either way, one can also filter to display only specific Unicode ranges such as Latin Extended B or Cyrillic.
(Some operating systems and font management applications have similar functionality.)
If you're unfamiliar with GID ordering, a few more words may be in order. The order to which glyphs are assigned Glyph IDs (GIDs) is essentially arbitrary. It may be standardized across fonts from one vendor (as Adobe does), and it may be deliberately controlled by the font developer, or seemingly arbitrary depending on the order they designed the glyphs in. It's really up to the person who made the font whether they control the GID ordering or not.