You can delete your own question. The option should appear under the tags, between close and flag. The real question is, should you delete your question?. Also note that we can only talk for Arqade. Blender.SE may have an entirely different stance on the topic, and the only real way to know in regards to an alternate SE question, is to ask on the appropriate SE meta.
In most situations, a closed question can still be salvaged. You need to ask yourself why the question was closed. Look at the comments, and especially at the close reason.
Duplicate questions should only be deleted for severe quality issues.
If your answer was marked as a duplicate, and you agree that it is a duplicate, consider your question as an extra sign pointing to the original question. Another user may look for the same answer, and fail to find the original question, but still find your duplicate. For this reason, duplicates tend to stick around, as a way of guiding users to older questions.
Too Broad and Unclear questions should be edited.
Either of these close reasons simply means that you need to provide more information, either to narrow down what your actually asking, or provide enough context for the users to properly answer it. Look at the comments, and see if you can address the queries being asked by users. Editing a closed question sends it to the reopen queue, so be sure to address any issue you don't see, yourself, as a comment.
For example, your question on how to claim land was closed as "Unclear". I had originally flagged the question1, as without an actual question in the body, I was not entirely sure what you were asking. In context of the provided answers, this is a good candidate for "should be edited", and I have done so and voted to reopen.
In this context, my advice would be to never assume a question is obvious, without actually asking it. While it might seem obvious, other questions might seem near-enough for us to be unsure if that is what you actually meant. It is also worth addressing that without a question mark (?), your making a statement; you are not technically asking a question. I believe this may have also thrown me off, at first.
Off-topic or primarily opinion-based are more likely candidates for deletion.
These questions are more likely to be suitable candidates for deletion. However, sometimes it is the exact wording you use that might close your question. Check meta for anything related to the close reason, and check the comments for meta links. Many users comment with meta explaining their reasoning, to help the user better understand why the question might be off-topic, and how to fix it.
Low-quality posts might meet suitable criteria for deletion, too.
Note that this is completely at your own discretion, but you may wish to delete poorly-received questions that are not candidates for being closed.
In almost every situation, you should have a look at the quality of your question, and address the down-votes with an edit, instead. Remember that spelling, punctuation and grammar are essential, as some users will down-vote, instead of suggesting an edit.
Sometimes, you post a question, and suddenly it has several down-votes, and no comments. The question receives little attention, and your not entirely sure what you can do to fix it. You can always ask here, in meta, but sometimes it just comes down to a conflict of opinion between you and the majority of voters. Remember that there is nothing wrong with conceding, in these situations. You will even earn a badge for it:
Peer-pressure: Delete own post with score of -3 or lower.
Also consider that once a question has a score of -3 or less, it will not appear to newer users.
1 I can not recall the context in which I voted on this question, but only that it has tags that I have had on my ignored list for some time. As such, I believe this was initially brought up in a review queue, whether for "low quality" or for an earlier close vote that was since revoked.