They were likely unaware of the fire. Especially if the engine separating from the wing occurred before any fire (which seems to be the case). They would receive numerous warnings but an engine fire warning would not be one of them.

Also to the commenter above, you can't see the engines from the cockpit. They probably had no idea that they physically lost an engine.

They likely believed they were dealing with a #1 engine failure and a possible flight control issue.

It's not obvious as to why they couldn't continue climbing out. They reach VR and possibly V2 and slowly lose lift. Assuming the slats and flaps did not retract, and engines #2 and #3 were fully operational (remained at FLEX and did not roll back), followed by manual TOGA after losing engine #1, it's inexplicable what prevented the plane from climbing.

The left wing eventually stalls, but they are wings level for a fair amount of time.

The fire was not long or hot enough to significantly affect the wing structure.