I am planning to upgrade from AEM 6.2 to 6.4. Below are the steps to perform in Author server.
Do we need to perform the exact steps for the remaining Publisher servers? or Is there anyone to replicate to Publisher after upgrading in Author server?
Upgrade needs to be run on each instance separately and make sure you are starting the instance with the correct run mode. EX: Starting author with "author" runmode
That said, you need to run repository migration between step 4 and 5. See detailed steps at 
Below link details the sequential steps for Author, Publish - TarMK/MongoMK with sample scenario.
Also, take care of repository migration using crx2oak tool (to accommodate the changes in Segment Node store introduced in AEM 6.3)
Each of the instances (author and publish) needs to be upgraded separately and the same steps needs to be performed across all the instances. The only difference with the command will be file name and run mode i.e. author vs publish and the port number.
java -server -Xmx1024m -XX:MaxPermSize=256M -Djava.awt.headless=true -Dsling.run.modes=author/publish,crx3,crx3tar -jar cq-author/publish-p4504.jar -c crx-quickstart -p 4504 -Dsling.properties=conf/sling.properties