How, if possible, do I delete questions and answers on my profile?
There is a delete button under all of your posts. If you click on it you will be presented with the option to delete it.
Here is a screenshot of what it looks like under a question post:
Once you reach 250 reputation, it will look slightly different because you will have the additionaly option of closing the question. But the delete button will still be there:
Here is a screenshot of what it looks like under an answer post:
Note that (as mentioned in the links provided by Isaac in a comment) deleting your questions that already have answers is improper, as it is unfair to remove other people's answers just because you no longer want your question. If you do click on the delete button on a question that already has answers you will receive the following message asking you to reconsider, and warning you about potential consequences:
If you still proceed with clicking the delete button then you will be able to delete the question if there is only one answer with no upvotes and no bounties. If there are multiple answers, or one answer with an upvote or a bounty, you will not be able to delete the question. Instead you will receive the following message:
Also note that even if you do delete a question or an answer, it will not be truly deleted. It will only be hidden from regular users. Any user with more than 10,000 reputation (or a moderator even with less than 10,000 reputation) will still be able to see your deleted questions and answers if they visit the page that they are contained in.
If you truly need to completely delete something or have your name removed from it (e.g. it contains compromising information), you can contact Stack Exchange and ask them to help you.