As @ToasterxB mentioned, the Google Noto Sans font family is a good option, as it's designed to cover a wide range of languages with a consistent design. It includes a font for Tamil, so it might be worth trying.
For the table of contents issue, sometimes converting the ebook to a different format (like EPUB3) can help, as it offers better support for international languages. Also, make sure your device firmware is up to date, as updates often include improvements for font rendering.
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