Your bike has perfectly ordinary 27 x 1 1/4" tires. People have ridden tires like yours for thousands of miles on all sorts of surfaces without problems.

Your tire exploded because it was not seated properly or because a piece of the inner tube had gotten trapped between the tire and the rim. Please read up on correct installation of bicycle tires, and give special attention to proper seating and adding air.

I'm not going to give you my thoughts on "everything" because, well, that's a lot.