I am new with Slackware, and have just downloaded Frostwire, but it's not supported as Slackware package, so I had to download the bundled tarball. The only problem is that whenever I want to run it, I have to open a terminal there, and then:
It's not entirely that this is a big deal, but I have to keep the terminal window up. Any way I can make this into what I think is called a daemon, where it starts then disappears, or starts invisibly alltogether? OR, someone can point me to a Slackware friendly version of this.

Basically what I'm asking is how can I make a shortcut to the .sh file that when I click on it, will run it in terminal, and then make that terminal disappear, and me not have 7 windows running.
Any help appreciated!

you can simply write a bash script that does has this in it:

then chmod it to 0744 and and you can call it whenever you want.

sorry about that i wasn't really reading what is going on this is the code you will need:

Thanks very much! I'm new to this, and even though I can figure most of it out by myself, I know Slackware and all Linux in general adores the Terminal, so best learn it now.

You should try out this frostwire slackBuild. It will build a Slackware package for you that you can install. See the SlackBuild HowTo and other documentation on the site if you are unsure how to use it. It works with many versions of frostwire and Slackware.