How Old Is Tamayo?

Tamayo is at least 500 years old, as she was shown thriving during the same time as Yoriichi Tsugikuni and was transformed into a demon sometime before that.

How old was Tamayo when she became a Demon?

Having stated to be turned into a Demon by Muzan Kibutsuji, she is at least over 400 years old.

Does Muzan love Tamayo?

Based on the familiarity in which the two conversed at the end of the story, and the fact that she was beside him when he fought Yoriichi, suggest that he did have some fondness for Tamayo, though why in never covered.