"Father" is God's eternal name, that is to say, it is not that once He was not Father but only God and then became Father, just, like we can say that He was not always a Creator of the universe, but became one when He decided to created it and actually created. Not so with the "Father" for He is always, eternally, naturally, essentially Father. Since so, then it analytically implies that He always, essentially, necessarily has also His Offspring, the Son, who is thus co-eternal to Him and as such also God, possessing one essence with Him, for all essence any son gets from father and 100% of this essence; in Father's and Son's relationship this essential begetting and essentially giving of 100% of essence is done eternally and infinitely, without any intrusion of process or time, thus the Son is eternally perfect (Hebrews 7:28).

Thus, yes, "I and the Father are one" means that both are God, possessing the same essence 100%.

"Father" is God's eternal name, that is to say, it is not that once He was not Father but only God and then became Father, just, like we can say that He was not always the Creator of the universe in a fulfilled actuality, but became one when He decided to create it and actually created it. Not so with the "Father" for He is always, eternally, naturally, essentially Father. Since so, then it analytically implies that He always, essentially, necessarily has also His Offspring, the Son, who is thus co-eternal to Him and as such also God (John 1:1), possessing one essence with Him, for all essence any son gets from father and not a part of it, but 100% of this essence, so that man Achiles' son Neoptolemus is 100% man, just like his father; yet, in Father's and Son's relationship this essential begetting and essentially giving of 100% of essence is done eternally and infinitely, without any intrusion of process or time, thus the Son is eternally perfect (Hebrews 7:28).

Thus, yes, "I and the Father are one" means that both are God, possessing the very same essence 100%.