1) What is the role of the Holy Spirit today?
2) What does it really mean by "indwell' vs "live in us" vs "body is temple of God"? Do they mean the same thing?
3) Is there a complete list of gifts that we can get from the Holy Spirit today?
4) Upon water baptism, what does the new Christian get from Holy Spirit? Is it just salvation? Does the Holy Spirit "indwell" at that moment henceforth?

Most of your questions have been addressed in other answers, articles, or sermons on this site. Rather than repeat them here, let me direct you to several. If you have a more specific question after reading them, please let me know.

Can you explain the indwelling of the Holy Spirit?
What are the gifts of the Holy Spirit?
The Gift of the Holy Spirit
Where Do You Live?
The Holy Spirit's Work
The Work of the Holy Spirit