Yes, possibly I don't know all the facts and I am speculating a little. But can anyone comment as to whether an A319 can land on a one-mile runway with a full tank of fuel?
Yes. Landing a fully laden A319 at sea level requires a shade over 2,200 feet useable runway length. However, I have never know a pilot completely fill an aircraft yet. (except Concorde - when Gatwick was paying the bill - lol!!!)
Takeoff, however, fully laden would require 6,180 feet - 180 feet more than Gibraltar's 6000 feet strip.
As you rightly say, Gibraltar is rather prone to sudden fogs (high gusting winds affect us badly too from time to time) and regulars are used to last minute diversions - a bitn like our Channel Islands customers really.
However, it is usual once we divert from Gibraltar to Malaga to stick with the ground transport plan for all sorts of reasons, some of them political. (Spain all these years later still deeply resents Britain having a "possession" on the corner of their country to control Mediterranean shipping.)
It may not appear so, but you are actually one of the more fortunate passengers. Many seamen bound for Gibraltar have documents that allow them to enter the UK (including GIB), but not Spain, so they end up having to come back to London and try again later!
We can but apologise for the inconvenience and I can confirm that you would have been entitled to refreshments under the EC directive. I can only guess that the staff in Malaga were caught off guard by the suddenness of the diversion - I'm not excusing this, by the way - merely offering what could be a reason.
The cabin crew and flight crew, beyond getting you safely on to the ground and into the terminal buildings wouldn't have the faintest idea what to do about organising transport or refreshments. Usually, the captain and first officer will contact the BA station manager and place you in his/her hands.
What happened to go wrong, I have no idea but if you bash an email off to Customer Relations, your experience will be investigated and any offer will be made based on the case's own merits.