Is there an easy way to put my own header at top with my logo to make it look more like a part of my site? Is WordPress something I can put directly into my site, or do I just have to make a link to it?
question 1. yes, you generally need to edit the header.php by replacing the current header with <img src="yourlogo.gif" />
question 2. WordPress can be your main site if you install it into the root directory. otherwise if you want to make it a link off the regular site, make a new folder in the directory, install wordpress in it, then link to the folder.