Strange (hardware?) issues with ubuntu

Strange (hardware?) issues with ubuntu

Sorry about the ambiguous title.
Basically, I've been trying to install ubuntu to dual boot alongside
windows 7. However, I've had strange outcomes.
I first tried to install ubuntu 13.04. After problems with it, I tried
ubuntu 12.10, with similar problems.
I seem to have issues with the graphics card and the wireless. More
specifically:
When I loaded the live CD (and after I'd installed) I seem to have two
desktops, at first "overlayed" each other (I had two power down icons,
wireless buttons... with one screen in the NW of the screen and another
"wrapped around" it). I only have one monitor plugged in; on display, one
shows up as Samsung 19", which is correct, and the other as "unknown". I
don't know what this other display is or why it's there. On ubuntu 13.04,
I couldn't remove this problem; I could move the display around so that it
wasn't visible but my mouse could move off screen onto it (although of
course I couldn't see it). Ubuntu 12.10 was more manageable and has turned
off this other display, although it still appears in display settings.
Perhaps linked to this is that in the details, or about this computer
window, it lists my graphics as "unknown".
My wireless connection, whilst working, tends to operate at terribly low
speeds. I have a netbook running ubuntu 13.04 which has no problems like
this.
I've also occasionally seen scrambled up orange desktop screens on boot,
although this tends to go away after a couple of boots. I had a few times
where the live CD failed to boot (I've tried ubuntu 13.04 on a USB and
12.10 on CD). Another thing I'd point out is that in the GRUB loader now,
I have two entries for the windows loader and, as well as some memtest
options, ubuntu, ubuntu recovery and "older linux versions". Perhaps this
points to me incorrectly installing in the first place?
At the moment, ubuntu 12.10 is on my system, and seems to run much more
smoothly than 13.04. For the most part, it is completely usable, except
for it's horribly slow wireless connection. I worry of course that, with
these strange issues, there will be many more lurking around that I can't
see yet.
I haven't given you too much information; please tell me what information
(hardware, terminal outputs etc.) I should give and how to get it (please
bear in mind that I'm totally new to linux). Given that I have several
issues, I will note my motherboard: it's a Gigabyte GA-Z68AP-D3 socket
1155, and that my wireless card is pretty old (windows failed to
automatically find drivers for it; I eventually found Ralink RT2500 ones
that worked).
I'm sure there are no hardware faults though, since everything runs fine
on windows 7.
Thanks