https://www.quora.com/Quora-product/How-can-you-add-a-new-question?share=1 :

To add a question generally, type your question into the "Search Questions, Topics, and People" bar at the top of the page, then click on "Add Question." A dialog will appear asking for question details and privacy settings. Once you are done filling those out, click "Add Question" in the dialog to submit the question.

You can also add questions from a topic page. Find the bar that says "Find or Add a Question." When you click the "Add" button from that bar, again a dialog will appear asking for question details and privacy settings. Click "Add Question" to submit the question.

You can also go to https://www.quora.com/question/add directly.

According to Adam D'Angelo via On Quora, why can't I see the original author on the question page (though I can in my homepage feed)?

We're trying to prevent people from answering the person rather than answering the question by keeping the asker off the question page.

If you're on a question page and you want to find out who added it first, you can click through to the "All Changes" link under the question details.

The “All Changes” link doesn't appear anywhere if you aren't logged in, but the URL is simple to construct (thanks to Michael Hampton for finding this): add /log to the question URL, e.g. http://www.quora.com/Quora/On-Quora-why-cant-I-see-the-original-author-on-the-question-page-though-I-can-in-my-homepage-feed/log?share=1 Scroll to the bottom (the page loads dynamically, so you may have to scroll down multiple times) to see “Question added by …”.