it forgets about the third link and only downloads the fourth one

Folks claim that making persistent greater than 8 is bad. I don't know how to define "bad" in this case.

["SHOULD NOT" means] that there may exist valid reasons in particular circumstances when the particular behavior is acceptable or even useful, but the full implications should be understood and the case carefully weighed before implementing any behavior described with this label.

I changed it within about:config and it worked. Maybe it needs to be in whichever file that manipulates.

When I click a link say via email, or shortcut or whatever, I want it to open a new tab not take over an existing tab or open a new window.

Open external links in new windows or tabs

If another program wants to display a web page in the default browser, Firefox will reuse an existing window by default, which means that it will navigate from a page you might be reading. To stop this, add the following code to your user.js file:

// Stop reusing active windows:
user_pref("advanced.system.supportDDEExec", false);

What about new tabs instead of windows then? If you prefer tabs instead of windows, you must also install Tabbrowser Extensions, a very powerful extension that enhances the functionality of the tabbed browsing. After installing the extension, follow these instructions (make sure you didn't forget to add the above code to your user.js file):

1. Make sure you didn't forget to add the above code to your user.js file.

2. Select Tools > Options > Extensions, select Tabbrowser Extensions and click Settings.

3. Expand the Category list and select the topmost sub-item (it's supposed to read Advanced Tabbed Browsing but the Category list is too narrow).

4. In the Window Mode drop-down listbox, select Use multiple browsers only when I open them.

Done! Now any link opened by an external program, such as your e-mail client, will open in new tabs.