Google, Firefox, I'm mixed up !

[BellaUSA]

I have a Firefox icon on desktop. I clk on it to bring up Google page which says, 'make Google your search engine'. I have to clk on the down arrow which brings up a drop-down list from which I choose Google. From this, I can finally get Google & type in what I'm looking for. What goes on here ?
I have a mess I can't seem to get straightened out. Thanks a bunch !

[Geek-9pm]

Try this.
Get rid of that shortcut on the desktop.
Start up Firefox and go to the Google site.
Then make a bookmark. Then drag the the book mark to the desktop.
Wait, here's a b setter explanation.
https://support.mozilla.org/en-US/kb/create-desktop-shortcut-website
Any website address can be made into a shortcut for the desktop. 

Create a desktop shortcut to a website
You can use Firefox to create a shortcut on your computer's desktop to a page you've visited:
    Resize the Firefox window so you can see both your computer's desktop and the Firefox window on the same screen.
    Click the icon on the left of the address bar (where the URL is shown).
    While still holding the mouse button down, move the pointer to the desktop, then release the mouse button. The shortcut will be created.

That should do it!