Well thats a cool question. But since slackware uses the linux kernel the question should be does the linux kernel support HP 15-af008AX Notebook.
the vmliuz huge pretty much run everything. But the there are many modules "drivers" also built to load.
I see this question all the time. Slackware linux uses a vanilla kernel. and rarely patches it unless advised from upstream security Linus team.
what you need to do is your home work on what drivers you need this is not a distro question this is a linux question. at any time slackware you may recompile pile the kernel in case you have some exotic driver you need. if your hp is an optimus chipp you will need to look at bumble bee slack instructions.
from those specs yes.
if you get a black screen press alt f2 because tty your tty1 may have froze or crashed. that sounds like an acapi problem.
or a boot configuration.
as for holding those buttons that is a bios thing it looks like.
please make sure your slackware is uptodate. the xorg for your intel graphics was rebuilt to handle some issues.
http://docs.slackware.com/slackware:slackpkg