Put a hashtag and keyword togather related to your content or subject in your tweet. If someone searches twitter related to your tweet, your tweet will be shown in the search results.
Optimizing your website from mobile's point of view is mobile seo. It includes increasing page load speed on mobile devices, making website responsive or creating a mobile version of your website. You need to search google for more information on this.
There are a number of off page seo techniques like social bookmarking, forum posting, directory and article submission etc. But in my view blog posting is the best way to get links.
Make your website attractive enough to make the visitors stay longer on it and visit its other pages. Put the right content, images, video etc. on your webpage and check if it makes any difference.
There is nothing like a perfect keyword density. Just increase or decrease it as per your requirement but to be on the safe side, 4 to 6 % keyword density is ok.