Can I make it so that when I sign in to an admin account, admin rights are granted without a password? Sort of like in Windows. It's annoying to have to type in the password every time I want to install something.

One reason Linux does not have nearly so many security issues as Windows is the requirement to enter a password to acquire root privileges (there are other reasons, also, but that's an important one).

I am not aware of any way to accomplish this in Linux, and, if there be such a way, I'm not interested in it.

Please, for your own sake and that of others, do NOT do this.
Thank you.

To only thing that comes to mind would be setting the desktop environment (gnome, kde, whatever) to log in automatically when you start the computer. But you'd still have to type in your password for any new applications you want to install (or other important setting that you want to change). As far as I know, only Windows allows for what you're asking. Not even on a Mac OS (which you can't say is unpopular) can you do that. You need to type in your password each time. So I suggest you get used to this and think about the solid basic security this implies.