I used a "homemade" header spreader to get a little clearance toward the front of the chain stays where the tire passes. It was needed when I put hookworm tires on my bike.
If there is not enough clearance after adding an axle nut like Damien suggests then a little additional spreading of the chain stays may give some clearance. I did this with the tire and rim on the bike. I slipped the spreader through the spokes.
You need to check whether the tire and rim spins true and address that if necessary.
It is very important nothing rubs on the tires. You do not want a blowout or tire failure going 25+ mph on a bicycle.....especially if it's preventable.
I would definitely replace the tire in the pic with a new tire.
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I am not well versed in bicycle frame terminology. When the more knowledgeable guys "talk" here on MB.com they usually use very specific terms in their descriptions. I have to refer to pics like this often...
