Re: why whenever I download a launcher, it remove browser shortcut links from the homescreen?
Welcome to Android Central! If you install an alternative launcher and run it, it starts with a blank or default homescreen setup, so it won't include all of the shortcuts and widgets that you have arranged on your stock launcher. Some launchers can import setups from others, but this doesn't always translate correctly.
Whenever you install a new launcher, you have to set it up the way you want. If you switch back to the stock launcher, everything should be as you left it; and if you switch back to the new launcher again, it will still be how you set that up as well.