If I join the circle faction, I would get better drops but I cannot sell those drops on the auction house?
Correct. Items dropped as a result of benefits from the Circle of Fortune will have a Rank Requirement on them and thus cannot be traded. In fact, all items dropped while in Circle of Fortune cannot be traded and this is indicated on the items.
If I join the merchants faction, I can still farm for gear but the chance for great gear is a lot lower than the circle folks?
Yes, MG players will have a lower drop chance compared to CoF players that have ranked up to at least Rank 3 or higher.
Can circle faction folks BUY from the Auction house?
No, CoF players cannot interact with the Bazaar or initiate player-to-player trades. However, CoF players, MG players or factionless players can still Gift items to other players in their party provided they were in the same zone when it dropped, or use Resonances to gift items to players they've played with for an extended period of time. Please note that Gifted items will still retain any faction rank requirements they have.
Also, I thought it said you could swap between factions, do you have to start from zero every time you start or do you maintain progress?
You maintain your Reputation and rank progress within a faction even if you leave it. So if you get to Rank 4 in CoF and decide to switch to MG you will still be Rank 4 in CoF if you return. Though, you'll have to unequip any item with a CoF rank requirement to switch to MG (and the same for any items with a MG rank requirement if you switch to CoF).
If I am in the circle faction, get a drop I don't need, salvage it, can I then swap to merchants faction to sell the salvage items or are those salvaged items locked out from the auction house too?
If by salvage you mean use a Rune of Shattering or Rune of Removal on a Magic, Rare, or Exalted item to gain Affix shards from that item then no, you can't trade those crafting items. Crafting materials are untradable.