Long time FT'er, first time in the BA forum...

We have about 240,000 Chase Ultimate Rewards that we'd like to convert to Avios for this trip.

Family of four, looking at MSY-LHR (non-stop) on 12/22/18 and LHR-MSY (non-stop) on 1/2/19. We've found decent premium economy pricing on BA.com and other search engines.

When I search on BA.com for availability of reward flights, it shows zero availability on this route for the entire month of December and January.

1. I currently have zero Avios. I don't want to convert my UR to Avios (yet) because the transfer is non-refundable. Is the zero-balance the reason I can't see any availability?
2. Is the conversion of UR to Avios one-to-one?
3. What are the estimated fuel surcharges on this route? I've heard they can be nasty.