Fix and tune ProfileSaver

- the statement to mark the profile saved was not guarded by the right
condition.
- increase the backoff to 2x and maximum period time to 10 minutes.

As part of this change also
- fix typos
- remove uneeded warning
- add more VLOGs for easier debuging in the future

Bug: 27914456

(cherry picked from commit 0cdaa6cd)

Change-Id: I76ddc6ced897bb91cfbd2a0cb6614bdeeafb9ee9