Can I update Joomla version?

Yes, but I can't Upgrade to 2.5.8, when I search for updates it doesn't show any update, when I try to install from extension manager it doesn't work too, how can I upgrade to joomla 2.5.8?

In control panel in left icons in last row you would see icon with ! red mark, you just need to click it. If that does not show up you joomla is up-to-date with last stable release and then better do nothing.

Can I upgrade to 2.5.11 ? it still shows to 2.5.8 as latest version , although 2.5.11 come out. Please advise.

Check first in extension manager under Database tab do you have some link that says something like click here to repair database if yes click on it.

After that try update. Update problems are more for core joomla forum that this