I think I missed why the 't' has to be exist here. Does it have something to do with starting with a vowel?
yes. It's because it's a masculine noun starting with a vowel. Therefore "t-" gets prefixed after an
How do you know it is a masculine noun
Because of the t- in front of it.
Can údar be used for a female author? In that particular situation, would it eliminate the prefixed "t"?
Yes, údar can also describe a female author. The noun itself is masculine, no matter the sex of the author being referred to, so the prefixed t- is used even if the author is not male.