Remove xml namespace while transformation using xslt - xslt

Question

I am transforming XML using XSLT and facing issue while namespace removal. If I remove xmlns it works fine.
Issue 1. It doesn't delete namespace from transformed XML
Issue 2. Doesn't implements other template I have in transformation.
My Input XML
<?xml version="1.0" encoding="UTF-8" standalone="yes"?>
<Catalog xmlns="http://example.com">
<Books>
<book1>Wise1 Otherwise</book1>
<book2>Great Expectations</book2>
</Books>
<library>
<Name> Forsyth </Name>
<city> Cumming </city>
</library>
</Catalog>
Expected Result
<?xml version="1.0" encoding="UTF-8"?>
<Import>
<Books>
<book1>Wise1 Otherwise</book1>
<book2>Great Expectations</book2>
</Books>
<elab>
<Name> Forsyth </Name>
<city> Cumming </city>
</elab>
</Import>
XSL
<?xml version="1.0" encoding="UTF-8"?>
<xsl:stylesheet version="1.0" xmlns:xsl="http://www.w3.org/1999/XSL/Transform">
<xsl:output method="xml" indent="yes"/>
<xsl:strip-space elements="*"/>
<xsl:template match="#* | node()">
<xsl:copy>
<xsl:apply-templates select="#* | node()"/>
</xsl:copy>
</xsl:template>
<xsl:template match="#xmlns">
<xsl:element name="{local-name()}" namespace="http://example.com">
<xsl:apply-templates select="node() | #*"/>
</xsl:element>
</xsl:template>
<xsl:template match="library">
<elab>
<xsl:apply-templates />
</elab>
</xsl:template>
<xsl:template match="Catalog">
<Import>
<xsl:apply-templates />
</Import>
</xsl:template>
</xsl:stylesheet>

Answer 1

I think you are missing the namespace declaration in the XSLT templates to match elements:
This is my try:
<?xml version="1.0" encoding="UTF-8"?>
<xsl:stylesheet version="1.0" xmlns:xsl="http://www.w3.org/1999/XSL/Transform" xmlns:ns="http://example.com">
<xsl:output method="xml" indent="yes"/>
<xsl:strip-space elements="*"/>
<xsl:template match="*">
<xsl:element name="{local-name()}">
<xsl:apply-templates select="#* | node()"/>
</xsl:element>
</xsl:template>
<xsl:template match="#*">
<xsl:attribute name="{local-name()}">
<xsl:value-of select="."/>
</xsl:attribute>
</xsl:template>
<xsl:template match="ns:library">
<elab>
<xsl:apply-templates />
</elab>
</xsl:template>
<xsl:template match="ns:Catalog">
<Import>
<xsl:apply-templates />
</Import>
</xsl:template>
</xsl:stylesheet>