Tackling the last bit of your post first:
You can configure Firefox to use any web address you like as your home page. To have Firefox open with Google, first (with only one tab open) go to
https://www.google.co.uk . Then click the three lines at the top right of your screen, followed by 'Settings' and then 'Home'.
Click in the drop-down box next to 'Homepage and new windows'.
Select 'Custom URLs'.
Click 'Use Current Pages'.
(Left-)clicking the 'M' at the top right of the page should bring up a 'Sign Out' option, just like the one I see when I click on 'C':
https://i.postimg.cc/C5bYL2pS/Sign-Out.jpg