The bad things argument is simple yet telling.
Old testament God, assuming his existence, lets bad things happen
because we offended him greatly in the garden of eden, by eating that apple. We lost our innocence, and sin entered the world. We were banished from eden, and forced to live in an imperfect world, which contained disease and nasty mutations.
It's the price we paid for disobeying God, we were cursed as such. So the bad things yes God allows them, even though they do not please him, it is his will. He gave us free will, we f**ked it up, we got the bad things happen. But we can come back to God's favour, learn to please him and get to heaven when we die.