1. I buy Border Village and gain Bridge. I can put them on top of my deck in either order (because Border Village's effect is on gain, not on buy).
I think this is already false (so 2 and 3 are as well). I cannot get Border Village on top of the Bridge because of the lose-track rule.
I buy Border Village.
I gain Border Village (move it to discard pile).
Two on-gain effects happen, I can choose which one happens first. I can first move my Border Village to the top of the deck or first gain a card with Border Village.
Let's gain a card with Border Village first.
I gain a Bridge (move it to discard pile, covering up Border Village, meaning that Travelling Fair has lost track of Border Village)
I can now optionally move Bridge to the top of deck.
For the Border Village gain, 1 effect has been resolved, and the other does nothing anymore because of the lose-track rule, so I cannot but Border Village on top of my deck.
Travellers fair is paid for then surely each gain thereafter is dealt with in turn ...i.e. Either to deck or discard. So bv is bought (eg) and put on deck then chose bridge (put on deck) ... etc etc.
Am I missing something.
When you gain Border Village there are two different effects that trigger, Travelling Fair's topdecking ability and Border Village's gain a cheaper card ability. You can choose the order in which you apply them. Then, when you gain Bridge, Travelling Fair's effect triggers for that as well.
If I choose to topdeck BV before gaining Bridge:
1. I buy BV
2. I gain BV to my discard pile
3. I topdeck BV
4. I gain Bridge to my discard pile
5. I topdeck Bridge
If I choose to gain Bridge before topdecking BV:
1. I buy BV
2. I gain BV to my discard pile
3. I gain Bridge to my discard pile. BV is covered up so Travelling Fair loses track of it.
4. I topdeck Bridge
5. I try to topdeck BV but Travelling Fair has lost track of it.
Either to deck or discard.
The card is gained to the discard first, then optionally put on the deck with Travelling Fair. This is called "visiting" the discard pile.