If the Brotherhood player trips a Hostile Locals domain counter, does he get to use his racial ability to 'convert' enemy units during this combat?

No. A Hostile Locals token is not actually GFs, and the Yin ability you refer to targets GFs.

It doesn't, though. You can use it if your opponent only has Mechanized units. The question is not whether or not they are ground forces, the issue is if it counts as an 'invasion combat' enough for the Yin ability to trigger. Moreover, I'm not entirely sure that they aren't ground forces - they can 'lose' ground forces in between combat rounds, so for the game's purposes they actually exist.

The key word is "opponent". As per the FAQ "Opposing forces are defined as forces controlled by another player". So the answer is no.

It doesn't, though. You can use it if your opponent only has Mechanized units.

I would be very intereted to know where you got the impression that this would be legal.

The Yin ability specifically says "Ground Force" and IIRC, MUs are not considered GFs in general. There are a number of effects which OUGHT to affect MUs (logically) and don't, simply because the effect says "Ground Force."

The exact wording is "Before an Invasion Combat in which you are the attacker begins, you may roll 1 die. On a 5+ your opponent loses 1 Ground Force and you gain 1 Ground Force."

Technically speaking, it doesn't require there to be a GF on the planet; the opponent just loses one and you gain one. If you can't fully resolve an ability, you resolve as much as you can.

However, the same could be said about the "opponent" thing, too, and the definition of "opponent" is "other players" (and not Hostile Locals or Custodians).

That said, the FAQ also does have a specific entry about Hostile Locals and Yin (page 10), and it directly says the ability CANNOT be used against Hostile Locals. So even if you wanted to apply the "as far as possible" bit, you wouldn't even get the GF (even if the Hostile Locals didn't lose one). Because of this, I think its safe to take this to mean that you can't use the ability at all unless:

- The enemy you are fighting is an "opponent' (ie, other player)

- The enemy you are fighting has at least one GF (so no MU-only defenses or undefended planets)

Someone could probably ask this to FFG, but I'm pretty sure that's what the response will be.

The exact wording is "Before an Invasion Combat in which you are the attacker begins, you may roll 1 die. On a 5+ your opponent loses 1 Ground Force and you gain 1 Ground Force."

Technically speaking, it doesn't require there to be a GF on the planet; the opponent just loses one and you gain one. If you can't fully resolve an ability, you resolve as much as you can.

However, the same could be said about the "opponent" thing, too, and the definition of "opponent" is "other players" (and not Hostile Locals or Custodians).

That said, the FAQ also does have a specific entry about Hostile Locals and Yin (page 10), and it directly says the ability CANNOT be used against Hostile Locals. So even if you wanted to apply the "as far as possible" bit, you wouldn't even get the GF (even if the Hostile Locals didn't lose one). Because of this, I think its safe to take this to mean that you can't use the ability at all unless:

- The enemy you are fighting is an "opponent' (ie, other player)

- The enemy you are fighting has at least one GF (so no MU-only defenses or undefended planets)

Someone could probably ask this to FFG, but I'm pretty sure that's what the response will be.

Yes to the first point, no to the second.

The second point was indeed answered by FFG in the past: http://boardgamegeek.com/article/10465309#10465309

"Do you gain 1 Ground Force unit from Yin racial ability if the opposing player does not have a Ground Force to lose? Example: Defending a planet with 1 Mechanized Unit. Also, does the opponent get a Gen Synthesis roll for the lost Ground Force?
Yes, you would gain the ground force even in your opponent did not have any to lose. Your opponent may attempt to use Gen Synthesis for this lost unit."