Learn Russian: Добрый вечер, папа!

While хороший means "good" generally, Russian time-of-day greetings like "Good morning" and "Good evening" always use the word добрый, which literally translates to "kind". So you are actually wishing your dad a "kind evening"!

The word папа ends in "а". Doesn't that make it a feminine word?

It looks feminine because of the -а ending, but because it refers to a male person, it is actually a masculine word. This means if you wanted to say "my dad", you would use the masculine word for "my" and say мой папа (not моя папа).

Is Добрый вечер used as a greeting or a farewell?

Just like in English, Добрый вечер is a greeting used when you first see someone in the evening. When you are leaving later on or going to bed, you would use Спокойной ночи (Good night) instead.

Is it too formal to say Добрый вечер to your own dad?

Not at all! While it is a standard polite greeting you can use with strangers or your boss, it is also perfectly natural to use with family members. You could also use the casual Привет (Hi), but Добрый вечер is a warm, standard way to greet anyone.