Thanks Ben, I tried this in gmail and I also checked on the Open as Window , so now have a different shortcut and it opens in a view without bothering to open Chrome as a full browser. Interesting. Also interesting, I can do a right-click on this new shortcut and I get the view of options - like pinning to taskbar - like Bighorn had shown, rather than the smaller view in the one I posted earlier. Am attaching the new right-click options.
But if I want to do more in Chrome, I still have to use the other shortcut, which is okay. And somehow, the Start button suddenly showed gmail under the Chrome icon (before I created the new one out of the gmail Tools), and I was able to pin it to the taskbar from there like Bighorn told me about earlier, and it opens it along with the whole browser. Since I created the shortcut via gmail tools, the Start now has two icons for gmail.
So now only the issue will be if all these will work without having to sign in first.
I guess I could consider the pin to taskbar issue as solved. Just haven't completely solved the issue of losing the automatic logins. I tried clearing my cookies a couple weeks ago, but have not done so since and I am accepting cookies. Afraid to shut down for fear of not getting the automatic logins next time.