Even though updated to 4 successfully Firefox keeps asking me to update to 4. Why?

Before going further try to confirm what version of Firefox you do have.

What do you see looking at about firefox from the help menu ?
I ask because your System Details are showing Firefox 3.6.17 not the current version Firefox 4.0.1.

If you turn off the option to display the menu toolbar do you see the firefox button in the top left and do you get an option to use [why are tabs on top?|tabs on top], both are features of Firefox 4.

It is not easy to find help articles, or even other posts at the moment there appears to be a problem / glitch in the search system.

https://support.mozilla.com/en-US/kb/Finding%20your%20Firefox%20version
If your Firefox installation shows 4.0 or 4.0.1 where the red circle is and the string at the button of the window shows - Mozilla/5.0 (Windows; U; Windows NT 6.0; en-GB; rv:1.9.2.17) Gecko/20110420 Firefox/3.6.17 - see this support article.

https://support.mozilla.com/en-US/kb/websites+or+add-ons+incorrectly+report+incompatible+browser

scroll down to Reset your user agent

I tried to down load 4 again. The question comes you are donloading a binary file Save ? I click on save and it is saved . Then what ? still it is 3.6.17 in about Mozilla!

Use the downloads manager,

1. by for instance (Windws) pressing keyboard keys Ctrl + J
2. use the option to open the containing folder, then click on and run the file.

You may need to ensure you are using an admin account, and possibly disable or set security software to allow the update.

See also

• updating firefox
• software update failed

Indeed. Then I click on the binary file. And it asks run? And I click and it is updated to 4.0.1! Because in the help when I click on about the screen shows 4.0.1 as the firefox version. Nobody could think it out that I am a user not a maintainer! Now should I delete the binary file?

There is normally no need to keep the update files.

It should be possible to set Firefox to run the updates automatically. (And some time in the not too distant future the updates will by default be run automatically and silently)

Current bug with Firfox 4 updates
Just at present there is a bug that is affecting some users and may be preventing some upgrades to firefox 4, see for instance thread Something is trying to trick Firefox into accepting an insecure update. Please contract your network provider and seek help. (&)