If you want to keep your old kernel, do not run upgradepkg, just run installpkg. Also, see the README notes in /testing for Pat's 2.6.13 kernel as you need to set up an initrd for that kernel (especially if you use reiserfs for your hard drives).
You will also need to edit /etc/lilo.conf to add a new entry for the new kernel, and then run /sbin/lilo to update lilo.
2) As with the old kernel, do *not* run installpkg if you want to keep the old kernel and alsa. Just install the alsa-driver-1.0.9b_2.6.13.x from /testing (alsa-lib, oss and utils don't change).
After booting with your new kernel, run 'alsaconf' to update /etc/modprobe.conf (the new file used by 2.6).
3) Do *not* upgrade the kernel headers to 2.6.x - the kernel headers should match that of which glibc was built against. In Slackware's case, as long as glibc is built against 2.4, then kernel headers should be from a 2.4 kernel, not 2.6. The only reason to upgrade is some drivers and software require 2.6 headers to build, but these cases should be fairly rare (I've never come across this problem). Therefore, unless there is some actual need for you to do so, do not upgrade the kernel headers to 2.6