PATROL Agent does not use the JAVA/JDK however there are some Knowledge Modules that requires java.

Example: PATROL for VMware vSphere KM, Azure KM, PATROL for AmazonWweb Services etc

BMC no longer provides Java 8.0 after the recent announcements made by Oracle about commercializing JAVA.

PATROL KMs support OpenJDK or vendor-specific JAVA versions.

Please check the below link for more details.
https://docs.bmc.com/xwiki/bin/view/IT-Operations-Management/Operations-Management/BMC-Infrastructure-Management-PATROL-Repository/imrepo10/Release-notes-and-notices/Java-support-for-TrueSight-monitoring-solutions/

A couple of JAVA versions are available on BMC EPD site to download and upgrade. JAVA is available for Linux and Solaris.
Contact IBM to download install JAVA for AIX versions.

It is fine to install the latest JRE and then copy that directory to the directory location in PATROL. 

Use any JRE installed on the server and update the Patrol directory with the installed JRE.

Saying that whichever KM uses Java, it should have the functionality to update the Java home path in it. for eg : VSM KM.

Another query if the BMCBPAInstallJVM directory can be deleted, which gets installed along with the Patrol.

This is mainly used with the BPA product and that too for installation and uninstallation.

Therefore, it is fine to go ahead and delete this BMCBPAInstallJVM directory.