Is it possible to take same copy of mysql database in another instance(periodically) in the same server?
Yes , what you need is a replication environment ! 
Where your primary server (Master) will receive all updates and inserts, basiclly all DML's and the secondary server (slave) will receive only select statements ! 
 Here is a link to an article showing you how to do this.
 As for the load-balancing , in my case i use F5 to do this for me ! Here is link of the article that shows how this is done ! i have to worn you is quite hard to setup this puppy ! 
 



To run multiple instances using MySQL you need to have a couple of things separate from the initial install on MySQL like data directory, init script and config file.
 Ok i will place the steps here : 
-all you need is for you complete them:


Create a new data directory
Create/copy existing mysql configuration file
Create/copy existing mysql init file to start/stop/reload etc on
this new instance


Edit the init file and make some minor changes to make it this instance specific - like port number ,instance name, take care at this step  !!


Install default tables for this new database instance

mysql_install_db --datadir=/var/lib/mysql_new --defaults-file=/etc/my_new.cnf --user=mysql
Start the new instance
Set password for this instance and connect to this new instance
Finally add it to server start-up list
And now setup your replication.