Where do I sign as the preparer of my elderly father’s tax forms? And how do I indicate that he prefers someone else to speak for him in case of an audit?

You can only enter a 3rd Party Designee in the Desktop installed program using Forms Mode.  Not in the Online version.  There is no question and answer steps for it.  It's on the Federal Information Worksheet, near the end of Part VI, at the bottom of page 2.

I suppose if you are using the Online version you can print it out and write it in.  But then you would have to mail it.

Turbo Tax is for self prepared returns.  You are just helping him.  You can't enter a preparer's name in it if you efile.   If you print it out to mail I guess you could physically sign it as POA or something.