Yes, it's perfectly ok for one user to post more than one answer to a single question. It's by design, not a bug.
A single user may have cause to answer a question 2, 3, 4 or theoretically even more times if they have several different solutions. If/when that happens, you wouldn't want all n different answers to be included in a single one, as it would clutter things up. Far better that separate answers can be posted.
The edit option is there to edit an individual post, so if there are multiple posts you need multiple edit buttons. The point of having that link isn't diminished by there being more than one answer by the same person.
If someone is posting duplicate/unhelpful answers (or posts that simply aren't answers), however, please flag them as normal.