Three conventions writers actually publish under, E. Ashcroft, Mira Winter, or simply Vane.
An initial and a surname, E. Ashcroft, is the most neutral byline available and has a long history of being chosen for exactly that reason, by writers who did not want a first name shaping how their book was received before it was opened. A full first and last name is the warmest form and the standard for commercial fiction. A single name is the most stylised and works best where the writing already has a strong identity: columns, poetry, criticism. The form is a signal, and picking it deliberately is part of choosing the name.
A pen name has to survive being searched. Check that the name is not already an author with books in your genre, because sharing a byline with someone in the same section is a permanent discoverability problem. Check the domain and the handles on the platforms you will actually use. Consider how it will be spelled by someone who has only heard it, a name that gets misspelled is a name that does not get found. And check your jurisdiction's rules on publishing and contracting under a pseudonym, because payment and copyright registration usually still need the legal name behind it.
An initial plus surname is the most neutral, a full name is standard for commercial fiction, and a single name is the most stylised. The form itself is a signal.
Yes. Search for existing authors in your genre, and check handles and domains. Sharing a byline with someone in the same section is a lasting problem.
Generally yes, but contracts, payment and copyright registration usually still need your legal name. Rules vary by jurisdiction, so check yours.