Dear teseo,
I figured out the problem.
In your first reply you were asking if there were any previous issues with the site, and I told about low disk space I got resolved thru php.ini.
Back then my hosting provider edited my php.ini to switch to PHP 5.6 from 5.4 (payments pro plugin works with at least 5.6). So back then the support team edited the memory_limit as 512M, whereat the file itself interpreted it as 512 bytes and not megabytes. I had figured out the problem myself (with help of GitHub) and edited that line in bytes.
Now, I accidentally checked that file again, and saw that the max_upload_limit was also set to 512M, i.e., same as before, it was interpreted as 512 bytes! So, I just entered the value in bytes.
As of now the images are being uploaded smoothly. I can't believe the solution was so simple, and I could not figure it out.
Anyway, immense thanks for your invaluable time, efforts and support, teseo!