It comes down to the definition of "tail pipe fire". A tail pipe fire is normally what you might call a "static fire" of unburned fuel accumulating in the tail pipe with little to no airflow through the engine, and this is normally during ground operations especially during starts.
The tail pipe has an overboard drain for this purpose, but it needs time to let the fuel out. This is why, during a start, the procedure may require the engine to be dry motored for a minimum time if the start is aborted. This is to keep pushing air through the engine, to help dry it out you might say, and let whatever unburned fuel has pooled in the tail pipe drain overboard. If you don't do this and try another start right away, you might end up lighting off the residual fuel in the tail pipe during the start... and a tail pipe fire.
Based on the Air India pics, that wasn't a "tail pipe fire" in that sense (pooled fuel), and was actually case of some kind of engine disruption or malfunction that let the flame move out of the burner can into the turbine section and tail pipe. This drives the temperatures at the turbine and tailpipe through the roof. You can see this by the melted turbine blades. A fuel control problem or air flow disruption problem farther upstream would be the issue here.
You may not get a tail pipe overheat warning in this case because the overheat detection loop (sensing wire) is usually around the section of tailpipe within the cowling, and with the flame originating from the burner can and contained in the tail pipe itself with the airflow, the sensing loops on the outside of the hot section case probably didn't get hot enough.
What should have been obvious to the crew however, was Inter Turbine Temperature (ITT) (or whatever turbine section parameter that engine measures) spiking through the roof at the time the passenger was seeing the flames out the back.
So to question 1: Yes, a "tail pipe fire" is normally a fire from pooled fuel in the tail pipe and is normally only on the ground (but on some engines, could possibly happen during an in-flight relight as well).
For question 2: A tail pipe fire in that sense won't occur in cruise with the engine running. What is described as a "tail pipe fire" in the article is actually an engine malfunction that caused the flame to move aft out from it's normal place in the burner can, into the hot section, but it doesn't involve fuel pooling in the tail pipe. Bird ingestion, compressor section malfunction or compressor stall, fuel control going haywire (dumping in too much fuel). See any videos of airliners ingesting birds on departure and that's exactly what you see.