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Where are the requirements to have ferrite number check mentioned?
Means this is critical as I know in stainless steel materials but where exactly it has been specified?
Is this a code requirement?

This is an important consideration. Yes, this is a requirement according to many ASTM standards for material sepcifications.
For example, A790 pertaining to ferritic /austenitic stainless steel pipe has got a mandatory ferrite content rang to be verified in the final product.
Mostly for the duplex grades, it would call for a mandatory check.
However, the construction codes ASME B31 and the inspection code API 570 does not ask for a mandatory check and rely on the material specifications call as and when needed.

The material part is clear.
What about the welding which is done. In what cases, ferrite testing/number check stands mandatory?
And if it is not mandatory, what are the other recommendations and what are their sources?

I would recommend you to go through Annex. B, C & D of API 582 in particular to understand the requirements of ferrite content check.
There are specific limits defined therein.
Additionally, the limits are defined for the base metals and the welds in ISO 17781, which has also been referred to in API 582.
Let me know if there is any specific requirement you may be looking for.