About the 'no home' ting: it means that the system couldn't cd to the user's homedir after assuming the identity of the user. Usually this means that /home isn't mounted, or wasn't mounted when you added the user, but you may have other reasons. Just make sure that the entry in /etc/passwd for the user accurately reflects their homedir, then 'chown -R user ~user' and 'chmod -R u+rwX ~user'.
To get a log of when the users logged on, there are many utilities. 'last' provides a short listing; the 'sac' program can analyze the logins in several ways and is probably more than you will need. I am not sure that listing the users' commands is legal (but I'm not a lawyer so don't ask me) or desirable. It's called 'process accounting' in Unix-land, so try searching for that term and see if you can find anything. Note that .bash_history was NOT meant for this purpose, so any non-trivial use of it will have problems. Carl