Since he has an active offer of $120 from the seller, moving the buy it now price does not effect his price at all. There is nothing fishy here.
It's legit. The seller may have had so many offers in a particular range that is somewhat below his initial BIN that by moving the BIN higher he may feel as though new offers will come in where he would sell the coin.
Yes it is. An auction is something where you bid against other potential buyers and the person with the highest bid gets the item. The buyers ultimately determine the price. In this case, they are selling at a fixed price. The "make of offer" option simply means the seller might be willing to negotiate the price...but it's still the seller determining the price. The seller can set their fixed price wherever they want...and they can raise it if they choose. They might still accept the lower offer price...but that's their call.