Yes, to the first part of the question and no to the reincarnation thing...
I read Matt 17:11-13 literally with some underlining understanding - the concept of a spirit within a human being.
John the Baptist was born WITH the actual spirit (type) of Elijah. As we have or are becoming into the image or the spirit of Christ through the Spirit in or WITHin our own natural spirit, so John was BORN with the exact spirit of Elijah, the SAME spirit, beside and WITHin his own natural spirit, of the Father from his conception...he had come indeed as Christ said. No pagan reincarnation process at all...
The Holy Spirit can create a new or existing spirit (of a person who 'lived' or still 'lives' today as Elijah) within any person's spirit from conception or over time within that person - as we are maturing in Yahshua's spirit today. YHWH is the Father of all spirits. He can create any type of spirit at will.
So within John's spirit at birth was the actual spirit of Elijah created by the Father of spirits. Yahshua sensed and recognized this spirit within John instantly, as his Father caused this understanding within him.
YHWH has a purpose before time and creation, and that purpose for John is obvious according to scripture.
APAK
You have a lot of beliefs there that are not scriptural.
On the other hand, I am not going say they are not true.
Reading the scriptures, it is the obvious that the connection between Yeshua and John is very significant, but yet not completely defined.
The storyline of who John was or personified leaves some questions.
There is also the question as to what authority, he had to forgive sins.
If you look into the Jewish religion, you will find that they considered Elijah senior to the Messiah.
As in more connected to the Divine....more significant....that is why Elijah was to announce and introduce the messiah.
One of the reasons for that, is because they believed that the messiah would be a human warlord king.
Between the testaments the Jews conducted many uprisings against the Romans, during which some of their military leaders were looked at very closely as possible messiahs.
Because Elijah was so close to the Divine, the suggestion is......that is why he had the authority to forgive sins. But that is a question that Yeshua refused to address.
Then again it is obvious that it was intended that John would play a part in Christ's ministry.