No, (I'm not, it's not). I'm here/here I am.
aqui or aqui estoy
Estoy aqui
In Spanish, if the subject is understood, it may be omitted from the sentence e.g., 'Yo estoy aqui' means the same as 'Estoy aqui.'
Debo pagarle aqui. Estoy aqui para pagarle/te (formal/informal)
Estoy (aqui) junto con mi mama
Yo estoy aqui para ti, mi adorado amigo
I am free, in the permanent state. Soy, I am, is always permanent for example, Soy Roberto I am Robert will never change, but Estoy Aqui, I am here, is an indefinite. To be honest you would never say Soy Libre because it can change it should be Estoy Libre.
Aqui estoy yo y represento*/toco* (a la guitarra) en un restaurante *act/play (the guitar)
You would say "I am very proud of you" in English.
"Estoy estudiando"
It means well good, here no more. For example if someone is asking how you are. You can say Pues estoy bien, aqui nomas haciendo mi tarrea. Which means I'm good, here just doing my homework.
Nothing, I'm at home.