1- This problem is not related to the hack. It's a vb/browser problem which sometimes happens. You need to clear your cookies manually once, then it will be fixed.. This cant be hack related because the hack does not change log-out sections of vb (in fact it does not change ANY part of vb, it's an independent script) and when you try log-out you still interact with default vb script.
2- Yes because your address is wrong. It should be:
show.php?pg=webquery_help
and
show.php?pg=webtemplate_help
3- After you fixed these issues, login to your CP, Choose Add new Webtemplate, paste your HTML source of your page into the box add the conditional I referred in the below message and you are done..
If you want to disable this page to non members add:
[cantsee]1[/cantsee]
to any part in the webtemplate, and now your page will be displayed to board members only..
Enjoy..