I have recently found out that my firefox is a bit cranky, in the options tab i have highlighted 'enable' for the download status bar to display the items downloaded. In addition the download window indicating the history of items downloaded are not showing the downloaded items, i am quite puzzled as i had set all the required settings yet return with undesired results. May i know how should i troubleshoot?

In options ensure you have the following settings:

On the Main Tab - Make sure there is a tick in Show the Downloads window when downloading a file.

On the Privacy Tab - Make sure there is NO tick in Always Clear my Private Data when i close Firefox

i have done the following as per say, but to no avail the browser does not seem to respond as it had been instructed to. May i know how should i proceed?

I would suggest using the "Clean Up" button. Sometimes it dramatically increases performance of that individual windows if you consistently download.