Evolution doesn't happen in a single day. Mutation of a single individual doesn't count as evolution (just my opinion). Evolution is defined as change of allele frequency in a gene pool. The 4 major forces of evolution are mutation, selection, drift and migration.

Mutation can be a force of evolution, but it is not an evolution. If the individual has bad mutation (let's say it is lethal). It would die fast, and the gene would not contribute to the gene pool. If it is a good mutation, ie increase it's fitness (higher survival rate), he has more chance to mate and this increase the gene in the gene pool in the given location.

Evolution is random. We might not evolve to have bigger brain and smaller mouth.

Yep. Natural selection.

talking biologically, the purpose of life (apply to all organism) is to survive and reproduce.