6
Yes, you can post extensions here that don't use the API. There are several scripts/extensions/apps posted here that use undocumented interfaces(example) or even screen scraping(example).
The extension must make use of the API and/or enhance one or more Stack Exchange sites.
Reference:
Stack Exchange APIs Terms of Use (Still applies, for the most part)
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3
Sounds like you are technically not "linking" the pages (to open in Chrome, Firefox, etc.). Google suspects you of "bundling" someone else's content:
We don’t allow apps whose primary purpose is to drive affiliate traffic to a website or provide a webview of a website without permission from the website owner or administrator.
The overall Stack Exchange ...
Only top voted, non community-wiki answers of a minimum length are eligible
