It seems that it is NOT working on my PC but are working with all browsers installed (Chrome, IE, Firefox, etc.).
This comment is confusing, as it seems to be contradictory. What is it not working on?
a Adobe Flash (32-bit was installed) although my PC is running in 64-bit
I suspect you are referring to the 'Flash Player (32-bit)' item listed in the Control Panel. If so, this is the Flash Player Settings Manager, which is a 32-bit application (but manages setting for both 32-bit and 64-bit versions of Flash Player).
For the 'application initialization error', I'll need to review the installation log files. Please review the FAQ Where do I find the Flash Player installation log on Windows? and upload the two files, Adobe_ADM.log and Adobe_GDE.log, to cloud.acrobat.com/send using the instructions at How to share a document . Post the link to the uploaded files in your reply.
You provided the FlashInstall32.log file. I need the Adobe_ADM.log and Adobe_GDE.log files.