1. No, customers cannot delete their account or their ads. The main reason for not wanting to allow someone other than the admin to delete content is for
SEO purposes, some may disagree, but this is for the most part, why it's not an existing function. You could potentially customize the theme, however I'm not aware of anyone who has done this, and can confirming that this is not a planned feature for the next release.
2. Do you mean, preventing customers from posting in the parent category? No, this is also not a standard option in ClassiPress, however I am aware of customers who have made this customization and it has been discussed in the support forums.
3. Currently no, there is no option for this, however it is planned for the next v3.1 release of the theme.
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