How do you re-sync the Master MySQL DB with Slave DB changes if the Master goes offline? MySQL Server 1 is running as Master.
MySQL Server 2 is running as Slave.

With both DBs online, they are in "perfect sync". If Slave goes offline, there's no problem if Master still online; they will go back sync once the Slave is online again.

Besides the server configuration, I redirected the connection (with JSP code) for the Slave DB if the Master goes offline (I tested of course with /etc/init.d/mysqld stop). 

When the Master goes back online, is there any automatic method to sync the Master with Slave updates?
One good way to pull off something of that nature is to set up Master-Master Replication or Circular Replication. This is not to be confused with MultiMaster Replciation.

Setting up Circular Replication is actaully very easy if you have setup  Master-Slave Replication. Here is what you need to do in order to configure it.

For this example, we will assume Master-Slave Replication is active but you will experience a bit of downtime (1-2 minutes):

Step 1) Add this line to /etc/my.cnf on the Master.

log-slave-updates

Step 2) Add these line to /etc/my.cnf on the Slave:

log-bin=mysql-bin (or have whatever the master has for this)
log-slave-updates

WARNING : Here is the brief moment of downtime !!!

Step 3) On the Slave, service mysql restart

This will activate binary logs on the Slave

Step 4) On the Master, service mysql stop

Step 5) Use rsync to copy the /var/lib/mysql folder of the Slave to the Master.

WARNING : Here is the longer moment of downtime !!!

Step 6) On the Slave, service mysql stop

Step 7) On the Slave, find out the last binary log

Step 8) On the Slave, find out the filesize of the last binary log

Step 9) Use rsync to copy the /var/lib/mysql folder of the Slave to the Master. This should be a faster copy.

Step 10) On the Master, edit
Line 2 of master.info with the last binary log of the Slave.
Line 3 of master.info with the filesize of the last binary log of the Slave.
Line 4 of master.info with the IP of the Slave.
Line 5 is the userid of replication user (DO NOT TOUCH) 
Line 6 is the password of replication user (DO NOT TOUCH)

Step 11) Delete all binary logs and binary log index file of the Master.

Step 12) On the Slave, service mysql start, wait 15 seconds

Step 13) On the Master, service mysql start

Step 14) On the Master, run STOP SLAVE; SHOW MASTER STATUS;

Step 15) On the Slave, run CHANGE MASTER TO MASTER_HOST='IP of Slave',MASTER_USER='userid of replication user from Step10',MASTER_PASSWORD='password of replication user from Step10',MASTER_LOG_FILE='binary log from Step14',MASTER_LOG_POS=LogPos from Step14.

Step 16) On the Slave, run START SLAVE;

Step 17) On the Master, run START SLAVE;

I performed steps similar to this for another StackExchange question I answered.

Give it a Try !!!