Regarding question #1, because it was another motor vehicle that hit your truck it would be a collision claim. If the at-fault vehicle had been insured properly then you normally would have been able to place a claim through that truck owner's property damage liability policy. You may be able to file against the event organizer's coverage.

With question #2, it if was vandalism or something other than a mechanical failure on the part of the tire then it would typically be cover by your "other than collision" coverage which is your comprehensive coverage.

To find out for certain if this second event will be covered by physical damages coverages check with your insurance agent.