<xsl:param name="date1" select="'$date1'"/>
  DONT KNOW IS IT NECESSARY TO SELECT IT HERE???!!!

It is not necessary.
 <xsl:param name="date1"/>
should also work. There will only be a difference if
you don't set the parameter, in the first case, your
style sheet will then use 'date1', in the second case
the value of $date1 will be empty.