.......... When a faulty transistor is replaced with a similar type one, ( when it’s not possible to find an exact one) what are the important factors to be considered?

 

Polarity, voltage, current, gain, frequency of operation, size.

 

It depends on the application. Can you post a schematic and/or or describe the application?

 

Voltage, current, package, gain (or gate capacity for mosfets). And maybe lots more depending on the circuit design&demands.

 

If the transistor is used in audio equipment it may be one half of a "matched pair". In this case you must replace both transistors with a suitable " matched pair.