As all of you have suggested and commented, I totally agree that install for BDE Engine on latest windows is very very buggy. However, I believe that its installation is the one that seems to be having problem not the BDE Engine itself.
As suggested by other question in Stackoverflow, I came to a conclusion that I should be able to take the extracted files from common\bde folder and link them to my software install. So, that whenever I install my software, BDE Engine files also get transferred into its folder on C drive. That it does. Also, I have created the registry file to update the registry accordingly for the BDE. It is mainly located in HKEY_LOCAL_MACHINE\software\Borland. To create the registry file, just right click on the folder and choose "Export" option. I shellexecute the registry file as part of the installation process.
It all works without any problem. Now, I don't have to deal with all these errors. My software is up and running. For now this is a quick fix but definitely going to get rid of it in the next revision.