Your questions addresses two issues, so let’s tackle them one after the other, but I assume you know how to define custom styles.
Auto-numbering with static text
Define a new paragraph style for the question line; give it name Question for example. Tune the settings (margins, …) to your likings. I’d suggest to set Next Style in the Organizer tab to Text Body or the name of a custom style for your <whatever content> paragraph.
In the Outline & Numbering tab, select a numering style (also called “list” style) from the drop-down menu for Numbering section, e.g. Numbering 1.
Click OK.
Note: I prefer to use existing built-in “list” style rather than to create a custom one because the built-in ones are seldom used and there is low risk of creating an incompatibility. But you can design a brand new one, it is just a little longer than modifying an existing one.
Now, open the selected numbering style (it is called a “list style” when you hover the mouse over the rightmost style icon in the F11 panel) with a right-click and Modify....
Go to the Options tab. Select how you number your questions from the drop-down menu Number: arabic, alphabetical, roman, … Fixed text is set with Before (e.g. "Question ", with a space after) and After (e.g. “:” with or without space, en-space or non-breaking space according to your language typographical rules).
In the Position tab, you can tune how the “number” is highlighted from the rest of the text, notably if you use tab or space between the “number” and text.
Click OK.
When you type a question, give style Question to your paragraph and you’re done.
Note: experiment with the various settings to tune the layout to your liking.
Table of questions
At the position where you want the table (index) of your questions, select Insert → Indexes and tables... → Indexes and Tables....
From the Index/Table tab, select User-defined and tick the Styles check box in the Create from area. Click on the ... button to choose the styled paragraphs to include in the index. Click on the Question style and move it with >> button from the Not applied column to 1 (index first level). Click OK.
Give a title to the table and click OK.
If you want to customise the appearance of the index, the other tabs of the dialog allow you to set various paragraph or character styles for nearly unlimited display aspect. Experiment.
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