That's the sort of thinking that helps them get caught. McVeigh was initially caught because his car didn't have a license plate and he had a concealed weapon. If he'd had an ordinary vehicle with a tag and no weapon, he wouldn't have been found so quickly and might have even evaded capture for years (even if his identity as the bomber were discovered).
He was always going to be the fall guy. The groups he was involved in was full of federal informants and agents. Why such elements didn't try to stop him is another question for a FOIA that won't be returned for 100 years.
A gun perhaps, not the same gun used in the murder, that would be dumb to be caught with evidence directly connecting you with the murder. This is America, getting guns is not that hard. Gun owners tend to usually own more than one.
Also you would want to carry a weapon in a manhunt only if you intend not to be caught alive, because firing your weapon in a manhunt would only end in one way for the hunted.
No, not at all. You're extremely unlikely to win a shootout in the event law enforcement catches you, and having a gun makes it much more likely you get arrested and convicted. But even if a gun seems worth it, it should absolutely not be the famous murder weapon you just used! I mean, JFC, keeping the distinctive murder weapon on himself was either incredibly dumb or something shady is going on with the story.