I use a secondary account for my primary use (friend of mine who is a mac enthusiast suggested me to not to use the admin account for my primary use). So when I logged into the MAIN ADMIN ACCOUNT (that I do not use), I found the notification at the desktop (after the usual warning before the boot), I clicked on REPORT and saw the log (added the log to the main question). After I quit the log and restarted again, voila! No warning now! Back to business as usual.
No, it cannot. Actually, there is no there is no drive-bay at all (standard or optical). The traditional, 2.5'' 9.5mm internal notebook drives (whether SSD or HDD) that you're thinking of are not compatible (internally) with this model.
This is what the solid state "drive" looks like inside late 2013 models:
As you can see from the iFixit photo above, the SSD is really just a stick of flash memory, connected via the PCIe bus. It's made up of 8 identical NAND flash modules (in densities of either 32, 64, or 128 GB). The 256 GB drive is pictured here. There are 8 32GB chips in total, 4 on each side. The chip density corresponds to the listed drive capacity, so 8x64GB Modules = 512 GB, etc.
Though it is possible to replace the SSD with a larger capacity one, there's currently no aftermarket upgrade available yet:
Unfortunately, the proprietary PCIe 2.0-based SSD in the "Late 2013" models is limited to a smaller "blade" option, but upgrade options no doubt are forthcoming, nevertheless.
Soon forthcoming, indeed.
Consider purchasing an external storage device, or exploring 'cloud' based storage options.
Best Answer
I believe Apple's position is a standard erase is good enough on SSD. In the article on secure erasing, they recommend enabling FileVault before you ever introduce any sensitive data to the drive so that you can just throw away the encryption key and not need any passes of erase to be secure.
That being said, in your situation, I wouldn't do a 3 pass erase on an SSD and I also wouldn't do a simple erase with no passes.
Instead, I'd turn on FileVault 2 (Assuming you have a newer OS) and then boot to recovery mode and repartition the drive. Be sure to not unlock the drive but simply repartition it to an empty HFS+ partition, no passes needed.
That ensures that each writable block is totally encrypted and randomized so that it's impossible to tell what was free space and what was files, let alone do data recovery.
The passes are a marginal hit on the drive's life (they are rated for hundreds to thousands of passes), but one complete wipe might be as much wear as three months of heavy use. What makes the passes worthless is they waste your time and are un-necessary additional wear on a consumable part (the SSD).