Yes. Wirewood Lodge's ability will go on the stack. Once it resolves, Timberwatch Elf will be untapped and the active player will get priority. Yamabushi's Flame won't resolve until all players pass priority, so your opponent has a chance to activate Timberwatch Elf's ability targeting itself.
Of course, there will need to be at least one other elf in play in order for the ability to actually save it from the 3 damage Yamabushi's Flame will deal.
Yes. The full sequence of events goes:
- You cast Yamabushi's Flame
- Your opponent activates Wirewood Lodge
- Your opponent taps Timberwatch Elf targeting itself
- Timberwatch Elf gets pumped
- Yamabushi's Flame deals 3 damage to Timberwatch Elf
Now, between literally every step there is an implicit "both players pass priority"; you can both still respond at every juncture. So, for instance, if you want to respond to his Wirewood Lodge activation with another burn spell, you could do so and probably kill it (causing all the other steps to be countered for illegal targets)