Qiyam namaz; Missing fard rakaats

If I am doing qiyam namaz do I have to do all 10 rakat also what is the niyyat at being of each rakat I’m making I assume it’s nafl?

I missed my fards for isha in Makkah as I arrived here I joined in 2nd Taraweeh then I didn’t understand when I joined so when the imams switched over I pray 3 2witr then I realise they began taraweeh so I joined completed then later I joined qiyam I did 4 prayers and realise I need to do 4 fard for isha I did them in between then joined the qiyam prayer I didn’t miss any qiyam prayer as you know qiyam is long then I prayed 3 Witr with imam again! Please tell me is this ok?