Move private headers out of /include folder

1. The /include folder is exported by export_include_dirs attribute. The
headers for internal use should be moved to another place.
2. Remove unnecessary #inlcude from public headers. So we can have a
compact .lsdump for ABI checker.

Bug: 144407448
Test: atest
Change-Id: I5bb0df02a1ccb70f0e91f4b77668ce54e0127f62