Tracking is mentioned only briefly, in/around the pages you mentioned, in both the PHB and the DMG. And as you pointed out, in the PHB and in the DMG it doesn't specify tracking as having any maximum speed.
On PHB page 181, under Travel Pace:
A fast pace makes characters less perceptive, while a slow pace makes it possible to sneak around and to search an area more carefully (see the "Activity While Traveling" section later in this chapter for more information).
This sentence, depending on how you read it, could mean that any "Activity While Traveling" (which is the section Tracking falls under) can only be taken while moving at a slow pace:
... a slow pace makes it possible to to search an area more carefully (see the "Activity While Traveling" section ...
However, several activities specify how they operate under different speeds, meaning this interpretation doesn't hold up.
Additionally, Foraging, another Activity While Traveling that points to full rules in the DMG, has the following statement (DMG page 111):
Characters can gather food and water as the party travels at a normal or slow pace.
It makes sense that Tracking would have a similar statement, but it does not, so for the time being there's no RAW restriction on tracking at a fast pace.
You can, however, interpret it as being RAI due to Foraging or due to the negative implication of the Barbarian ability.
You are correct. If you were in total darkness, that would be equivalent to Dim Light/Lightly Obscured to a creature with Dark Vision. However, you would still have to make a stealth check to hide, as the wording is "You can try to hide..." (bold added for emphasis).
Hiding (PHB p. 177)
"When you try to hide, you make a Dexterity (Stealth) check...."
Best Answer
This effect is not dependent upon Raging
In the 3rd level Totem Spirit benefits, all three entries start with "While (you're) raging." These effects are obviously only active during Rage. The 14th level benefits are also worded to only be active "While you're raging".
The 6th level benefits simply state "You gain," and make no mention of the abilities being tied to rage.
Since there has been no published errata on the subject, the rules are interpreted as they are written - you permanently gain the chosen bonus.
The PHB states that using a spyglass magnifies objects to twice their size. A normal character would not be able to see further using a spyglass (RAW), only able to more accurately discern what he/she is viewing. While I would personally ask your GM beforehand, there appears to be nothing prohibiting you from being able to use your increased ability to see detail combined with a spyglass.