You need to avoid internal competition while selecting keywords for the internal pages.
It is unavoidable using the same word for the home page to give overall idea about the site to users and search engines.
I would suggest a couple of steps to rank your preferred page for a specific keyword:
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checking anchor texts of internal and external links. "Yoga mat" page to get link for the anchor text "yoga mat".
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usage of keyword in the URL and position of keyword in the title
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checking usage of keywords in the headline, image alt tag and image title
Answers to your questions:
1. Identify the top traffic driving keywords to your site. You may use them in the home page title but don't acquire links for the home page using these keywords which may develop internal competition with your home page and internal pages.
2. Title length is very limited. So use the space appropriately.