Again the simple right click solves all lol, at least thats what I use, simply right click on each window you want to close, and then select Close, job done.
The intuition, or trying to understand such things, can lead to headaches, as such I try not to think about it if I can help it lol, often it is obvious, but there are times where it is such a different way to look\think about something, you will never get it, at least until the penny drops, at such times I just plod on, and once in a while something will make sense, then parts fall into place, but thats me.
Now we all know that m$ puts it's own stuff to be used with the OS, but it doesn't always mean it is the best, or easiest, personally I use VLC as a media player, it can play pretty much anything you throw at it, and once you have set it as the default option, it will be the one that launches for media it is the default player for, in Win 8\8.1 the first time you access media\App's it will come up and ask you what you want to do with that specific file\type, and will offer suggestions as to what will run it, once you select and accept a specific program to work with such file types, it will become the default, repeat as each new media comes up, and you're good to go, hope this helps a bit at least.
*edit
I missed that you asked how to find the media player, personally I just launch the media file I want to use, the media player fires up automatically, so I never need to launch it in it's own right the way you're asking how to, but if you install VLC, by default it leaves a shortcut on the desktop for you, if you want to go in the other way, click on the Start button, if it isn't in view there, click the Down arrow (small icon in a circle) to list all the programs, and you should find it listed in there, but it's presentation doesn't always make it easy reading.
Another tip for you, to tidy up the Start page, if you right click on each item that you do NOT want to have showing, maybe because you have no interest in it, it will leave a tick on it, and open a small menu bar at the bottom, once you have clicked on all the items you do not want, look to the bottom and select Unpin from Start, something like that, those items will be removed from the start page, but remain installed.
Using the exact same method, while in the expanded list of ALL your programs, right click on each you WANT to have fast access to, again it will do the same as previous, when done, at the bottom, select to Pin these to the Start Page, something like that, then those item will be showing on the start page, hopefully this will make things a bit easier for you, you can also drag and drop the "icons" on the start page into any position you want.