Adsense code problem

Why is the adsense code showing up in these two situations?

* I have added the adsense code to a few of my posts through the html section on the post. If a reader clicks on the categories section on my site the adsense code is showing until you click on the post.

Also

* I have my site listed with a few site directories and I notice that when they list my most recent posts that this adsense code is also showing until they click on the post.

Another question:
We have our permalinks set as just post name. Why are is there a structure showing /category/post title/page# ?

Thank you,
Christine
http://www.womenshomeactivities.com