(Your question is a little vague: if point 1.) is HBA Firmware, and 4.) is HBA Check, what exactly do you want to check about the HBA? Existence? Link state? Speed? WWN? All of the above?)
You should start with the 'lspci' command, to verify that the card is actually present.
In Linux, all drivers (including HBA drivers) are usually kernel modules.
Once you know the name of the driver module that handles your HBA, use "modinfo <module name>" to view (among other things) the version number of the driver module.
Common FibreChannel HBA driver names are "lpfc" (for Emulex FC HBAs) and "qla2xxx" (for Qlogic FC HBAs).
To verify that the module is loaded, use "lsmod".
Linux kernel major version 2.6 introduced the /sys pseudo-filesystem. In the earliest 2.6.x kernel versions, the /sys filesystem conventions for FC HBAs were still taking shape, but with practically all modern kernels, you'll find information on detected FC HBAs within /sys/class/fc_host/host* directories. For each detected HBA, you will find at least a link that points to the /sys/devices sub-tree; this link will allow you to identify the HBA by its PCI bus ID.
From the /sys/class/fc_host/host* directories you will usually find the WWNs of the HBA, and the link state information (is the card online or not, and which speed is it using).
In a sense, Linux treats FC HBAs as a subclass of SCSI controllers. If the information you're looking for is not at /sys/class/fc_host/hostX directory, check the respective /sys/class/scsi_host/hostX directory too. The card model information and HBA firmware version number can usually be found here.
Before 2.6.x kernel series, much of this information used to be available at /proc/scsi/<module name>/* as text files with module-specific content. With the early 2.6.x series this method was still used by some drivers, but eventually all drivers were switched to use the /sys pseudo-filesystem.
Regarding PowerPath: it is installed using RPM packages, and the RPM package name includes the version number.
So, you could check the version by using the "rpm" command like this:
rpm -qa |grep ^EMCpower
If the PowerPath is currently installed, you can also have PowerPath report its version number by using the "powermt version" command.