Could someone please explain how I can determine what wheel sizes my bike will accomodate?

I have the 2006 Devinci Sydney (with disk brakes) - https://www.devinci.com/2006/eng/bike...rid/sydney.htm

It shipped with 700x32C's. I am wondering if it could take 35C's, but am not sure how to tell.

Your weblink gives you the answer! Go back to it, click on the frame icon, check the specs: "max tire size 35." There you go! Cheers.

Ok, so I'm a little slow for missing that. lol

...so a larger tire on a wider rim doesn't mean the wheel itself needs to be wider?