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Is my Schengen visa still valid?
Yes, it is still valid. Since the conditions underwhich the visa was issued have not changed, there is no reason to revoke it.
Will it still be valid after my residency expires?
Yes.
Can I use it to enter and travel Schengen zone [Area] countries while waiting for my residency extension request is approved (or not)?
There is no need, since when extending a residence permit, the residence permit itself remains valid (even if the date on the card states otherwise) until a decision on the application has been made. Depending on the country, some form of confirmation that the extension of an existing residence permit can be issued.
Note: this does not apply for the initial application of a residence permit.
For 3rd country nationals that require a visa to enter the Schengen Area, an existing Schengen (or National) Visa can be used to travel to other Schengen countries during the initial application of a residence permit.
For 3rd country nationals who do not require Schengen Visa can travel to other Schengen countries with their passport.
In all cases, the confirmation of the application in progress, togeather with their passport, serve as a replacement for the (possibly outdated) entry stamp which otherwise shows how long the visitor may remain in the Schengen Area.