Can an unwanted post in a Discussion be deleted?

Yes, posts and replies can be deleted by:

 - The 'admin' permission per Topic as set on the front end by a user with edit rights (Topic > Edit)

 - The 'admin' permission for every Topic (as given in Admin > Discuss > Permissions)

A user that fits the above scenario(s) can delete a single post straight away using the 'delete' function:
 

However, if there have been replies to the post these will need to be removed first before the ability to do so for the original comment will appear under it.

How do I pin something to the top of a Discussion?

It is not currently possible to pin a comment in a discussion, but a workaround is to edit the description of a Discussion topic and put in the link/information you wish to be 'pinned' as it will always show at the top: