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Depends on what you can live with. I just pulled 31 x 10.50's off and there were rub marks on the radius arms, caused by it rubbing at about 3/4 lock. I put 30 x 9.50's on and there is no rubbing.
If you get aftermarket rims, it makes a difference also. They usually stick the tire out farther from the truck, helping rubbing issues. I would not put a very wide tire on a stock rim anyway. It wears out the middle of the tire, the stock rims are usually only 6 inches wide.
Depending on what you consider fitting, you can do a 35, it will rub things at full lock but 99% of the time it will be fine. A 33 is a decent fit.
Again, an aftermarket wheel is a very good idea.
True, but the effect is the same - too wide will rub on leaf spring.
Also be sure to consider the effect larger diameter tires have on the gearing. Bigger tires = less gearing.
See:Differential Gear Ratio Chart - Tire Size to Gear Ratio