multiple requests shut down mysql
The comment from Barmar is correct.

You do not have enough memory in the server for the InnoDB Buffer Pool.

Since you got the message

140107 0:09:29 InnoDB: Initializing buffer pool, size = 64.0M


followed by 

140107 0:09:29 InnoDB: Fatal error: cannot allocate memory for the buffer pool


you should lower innodb_buffer_pool_size below 64M in /etc/my.cnf and restart mysql.

SUGGESTION: If it is withn your budget, you should setup Apache and PHP on a separate server. Connection all webserver requests to the DB thereafter.