Question:
Can an individual in his home say Anim Zmirot or Avinu Malkenu?
Answer:
Regarding Anim Zmiros, I haven't seen anything on this, however it is usually only said with a tzibbur and not individually. We are allowed to say Aveinu Malkeinu even if we don't have a minyan.
Have a gmar chasima tova
Sources:
Shitas Kamai Yuma 87b, Mesores Moshe 253.
