In the process, the hard drive that I ordered (Seagate 2TB Firecuda SSHD) had a problem. Its Head was making loud clicking noise and used to hang when reading from or writing to sectors on the disc. This certainly had an issue and I had to immediately buy another drive and went for the Samsung EVO 1TB SSD. Now I am running on two SSDs, the mSATA 500GB for the OS and the other regular 2.5inch 1TB for the data/programs. The Seagate drive will be sent for replacement, probably I will be using it for storing videos and system backups.
I see that the system is booting little faster than usual(with SSD Caching as it was previously). Programs are loading way faster and installations are instant. This feels great, and the system is soundless.
Only thing that I am worried about is that the temperature on mSATA is peaking to 60c at times when there is many I/O operations with the OS partition. The system fans are kicked up to cool, but this happens gradually and the fans are not throttled immediately, rather a while later.
Regarding the RAM, all RAM Cards, 8GB each are working fine. Complete system diagnostics are also positive, and there are no more issues except for the weak battery, for which I have consulted DELL team for replacement. They have agreed to do that on a reasonable price.
That UNEXPECTED_STORE_EXCEPTION BSOD was probably occuring because of the faulty hard drive that I had and this was also enabled with SSD Caching. From the day I disabled that SSD Caching, I did not see that error again.