I ask my own questions. Only I know what my story is about and what character traits are relevant to that story. When I try to ask generic questions that I have found on the web (e.g. "What is the favourite food of your character?"), the answers are usually meaningless to my writing.
I have looked at character software, but I found that their preconceived structures of character relations (e.g. protagonist-antagonist or hero-sidekick) or their pseudoscientific concepts of personality (e.g. the Enneagram) have more stifled by creativity and made my stories generic and unoriginal. I sometimes do use some random lists of character questions when I need inspiration, but once my imagination has been sparked, I quickly abandon them and let my mind roam free.
###If you want to be original and creative, then using another person's concept of character will hinder you.
I take writing to be a dynamic process. I don't have to answer all questions about all my characters before I begin to write. I can always stop the writing and answer further questions, as they are raised by the advancing plot. I have found that I rarely had to rewrite anything I had written before because of these new Q&A.
To keep my characters organized I use a spreadsheet app (Excel), because it allows me to ask the same question (row) of all characters (columns) and see their different answers side by side and compare them. I can even easily highlight certain columns that currently interest me the most, or rows (story archs that I'm working on), or rearrange rows or include images. A spreadsheet app works better for me than a text editor (Word), where relations between pieces of content are difficult to visualize.