1: I have a Barclay US World Elite card that is supposed to function in Europe and, I'm told by Barclay does not have fees for European
purchases...
If Barclays says your card has no FTF then it doesn't. You should be able to confirm that by looking at their web page marketing the card. The transactions failing have nothing to do with any transaction fees. It might be this...
Whenever a US credit card appears to be failing for a European transaction, but there's no suspected fraud, no "decline", no evident reason it's failing, and the card-issuing bank, and everyone else involved says there's no problem, it should go through just fine but it won't...I usually suspect an obscure but widely used technology called "3-D Secure." It's a security system often used by companies that process European credit card transactions. Staff at your bank and the merchant trying to charge you may be oblivious and know nothing about it. Here's an old thread about it you may want to review:
3-D Secure credit card payments - wha???
This thread was started several years ago (when I first ran into this). 3-D Secure is still with us, though it seems lately to be less of an issue, and now it can be managed if you are able to reach someone at your credit card company who knows what they are doing. Barclays is an odd bank (they have many quirky behaviors you rarely find in bigger, more well-known US banks and credit card issuers). Your issue might not be 3-D Secure, but what you are describing sounds exactly like the way 3-D Secure makes transactions fail (that is: everybody on both ends of the transaction says, everything looks OK, it should go through, yet the transaction fails...your bank says they are NOT "declining" the transaction, the transaction just "fails" at some intermediate point. Everyone shrugs and says "maybe try it again", rinse, lather, repeat).
Short solution: try another credit card. Some cards handle 3-D secure seamlessly, some fail completely and mysteriously.
2: International monetary transactions, perhaps to only me, seem to be in flux. Whether they are or not, in order to minimize fees should I Pay in Euro or US$ both when I'm booking on line and paying while in Europe?
Always, ALWAYS A-L-W-A-Y-S pay in the local currency. Never accept an offer to pay in dollars. This is a common (probably the single biggest) scam on foreigners in the world. Look up "Dynamic Currency Conversion" aka DCC (there are countless threads here on it...enter "DCC" into the search box and feast your eyes...).