The sequence
1) Aborted/baulked landing with go-around.
2) Gear does not retract.. fly aircraft follow MAP
3) At this stage A/C is just declaring a go-around as there is no fire yet..
4) Ecam started several checklists plus cabin reports
5) Engine Fire starts, change priorities and start memory items
6) Decide on RW 35 as best option, declare May Day, rest is history..
In this time line 12 minutes is not long, the suggestion the aircraft was flying around for 20 minutes on fire is not accurate.
Old system Aviate, Naviagte, Communicate..
Ataturk is a swarming nest of aircraft with holding on arrival the norm. Even in CB activity it is difficult to get avoiding tracks due traffic density, so in this situation above ATC have no Idea what's going on until the Pilots tell them.
As for " vectoring over water" why? to avoid built up areas" crew took shortest route back to land, RW05 was not a good choice, they did well. ATC also did a good job in getting the diverts away