I generally recommend having HJT 'fix' all O16 entries simply because it is easier then researching all of them individually and doesn't hurt anything -- any legit entries will come back next time the site is visited. Doing this can sometimes make a big difference in the length of a log as well.
The poker programs often come with a lot of adware (and sometimes spyware), and users usually aren't even aware they are installed on their systems. As long as your mother is aware of the risks, and doesn't mind the ads, there should be no problem.
You may want to do a search here on DaniWeb for comments about Limewire.
Your log looks clean to me now, happy computing :)