There are two totem "systems" for barbarians: The one from Complete Champion, and the one from Unearthed Arcana (which is in the SRD too). While you explicitly can't take multiple totems within the same system, you can technically take them
between the systems so long as the class features can still be swapped, such as with the Lion Spirit totem from CCh and the Wolf totem from UA which do trade different abilities. However, your DM might call BS on this for whatever reason, so run it by your DM first to make sure it's okay.
The rules for
reach weapons explicitly say they double the wielder's natural reach, unless otherwise noted like with the whip. The natural reach of a
tall large creature is 10 feet, which means it having a reach weapon allows it to threaten the 15 and 20 foot ranges instead. No, this is not "typical math" because it involves the actual squares on the grid. In the case of a creature's reach, having a 5 foot reach (1 square) would double to 10 (still 1 square, just further away), but having a natural reach of 10 means its reach is 5 and 10 (2 squares), thus doubling it means it can attack stuff 15 and 20 feet away (also 2 squares, but further away).
Of note with that is
dragons are long creatures, so their reach is shorter except for their bite attacks which are explicitly shown as being longer.
