My question is:

Would I have any problems installing the openSUSE 11.1 (i586) DVD on a i686 OS?

Here's my system information:

OS: Linux 2.6.18.8-0.13-default i686
System: openSUSE 10.2 (i586)
KDE: 3.5.5 "release 45.10"

More specifically, i think my architecture is i686;

1) I'm not sure how to figure out whether my computer is i686 or i586.

2) If I were to install openSUSE 11.1; I only see the .iso for i586, would it be okay to install on my current computer.

3) If i'm asking all the wrong questions; please point me in the right direction.

Thanks in advance.

Its unclear what you mean by "on a i686 OS"; if you do a straightforward install of OpenSuSE (of whatever version), that would be the OS; if it is the OS (and putting aside things like virtualisation, which I assume that you don't mean) and therefore it can't be a problem that it is different from something else.

Assuming that you mean "installing the openSUSE 11.1 (i586) DVD on a i686 hardware", the answer is no, that will not cause problems.