It may help if you post screenshots showing the problem

• How do I create a screenshot of my problem?
• How to make screenshots

You appear to be posting from Windows XP and that defaults to showing the menubar toolbar.

• Display the Firefox button menu instead of the menu toolbar

Windows 7 defaults to a newer system that displays a Firefox button.

Not sure about why the new-tab icon should disappear. A screenshot may help. It is often easy to reset, but that could result in intentional customisations being lost.

Try in Firefox's safemode, also temporarily disable any plugins, and use only the default theme.

• Diagnose Firefox issues using Troubleshoot Mode

If all else fails, or you're in a hurry, you can remove your existing toolbar customizations and re-customize using the following technique:

Open your current Firefox settings (AKA Firefox profile) folder using

Help > Troubleshooting Information > "Show Folder" button

Keeping that window open, switch back to Firefox and Exit

Your profile folder window should come back to the front. Pause while Firefox finishes its cleanup, then rename localstore.rdf to something like localstore.old.

Restart Firefox. Return to customizing to complete the job.

By the way, the Bookmarks drop-down button does have a disappearing act: If you show the full classic menu bar with the Bookmarks menu, the button is removed from the bar, perhaps on the theory that it's duplicative in that configuration. There may be a way to override that with style rules (much of the toolbar area can be modified that way), but I don't have a recipe handy.