I want to create a WP blog that will sell ebay items from a certain Major League Baseball(MLB) team. Am I allowed to do this at all? If yes, under what circumstances? Can't use their logo?, etc.
You can sell the merchandise as long as you legally own it. However, using the logo for commercial purposes most likely legally requires the permission from the MLB and the team. Furthermore, most teams are not going to come after someone blogging about them, as it just looks bad. If you want to play it safe though, best idea is not to use the logo.
I have no idea about MLB, but the Premier League ( in England) takes matters quite seriously. You cannot display the logos of clubs on your site, and cannot use their fixtures on your site ( unless you pay and have permission ) According to me, you could sell the items as long as you're not giving the impression that they are buying from the official site. You could probably use some promotional e-bay material, but I'd advise not using the logo without permission.