Linux commands....
 

Can you rename and move at the same time using the mv command?

Also

My Linux+ book says that the chown command can be used to change user and group ownership. I can do the former but not the latter. I guess it is wrong.

mv ~/xxx /tmp/yyy for instance?
Yes.

Sure you can change both at a time with chown.
Of course not to a user/group that you're not/no
member of ...

like:
johnDoe@localhost> chown janeDoe:bin .bashrc
won't work ...

If you're root 'tis a whole different story.... :)

Cheers,
Tink

use

chown user.group file

obviously you must have permissions to alter the ownership in this way