Silverarrow

Does Silverarrow’s gold allow her to fast travel into/out of the battle zone? Or does it follow the normal restrictions for fast travel?

General approach to reading all the card texts is read it literally and if something isn't mentioned, then it's not there.

For Silverarrow’s silver, does the friendly hero have to start their movement action within radius to ignore obstacles? If a friendly hero starts their movement outside radius but then moves within radius, can that hero ignore obstacles?

Movement actions don't check active effects mid-move.

Can Silverarrow play her silver (which lets her ignore obstacles when performing movement actions) on the first turn, and then on turn 2 fast travel through an obstacle?

Fast travel is not a movement action.

Can Silverarrow's gold card target an adjacent unit? Does "maximum range" mean "the farthest enemy in range"?

If an ability is Range 3, the maximum range is 3. Meaning you can target at 1, 2 and 3. At maximum range however is exactly 3. Not 1 or 2.

Silverarrow's gold card doesn't allow Fast Travel to a space in her current zone — it must end in an adjacent one (and meet Fast Travel requirements for both zones), correct?

Yes, that's what an "adjacent zone" means.

Is there a rule about not targeting yourself? Can Silverarrow target herself with her alt green upgrade to get a card out of her own discard?

Page 10 of the rulebook.

Can Silverarrow go through the 3 obstacles near the enemy base into the jungle when fast traveling if silver is active?

Ignoring obstacles has no effect on zone adjacency.

How many times can Silverarrow move with her Ultimate when playing her level 3 alt red?

Once before the action, once before each repeat.