So, i'll address what you listed here first then once i'm given access to your adwords account, i'll be able to come up with more recommendations.
1) For quality score, one needs to make your keywords, Ad text and landing page text similar in context. The usual problem is using too many keywords in one Adgroup, this will cause keyword mismatch as your Adtext and Landing page text can't always be similar to too many keywords. Solution, separate keywords of different products into different Adgroups and direct the ads to a more suitable landing page.
2) Saving cost, i would like to believe you have conversion tracking installed. This will let us know the campaign, adgroup or keywords that are bringing in conversions. We will need to concentrate most of our efforts on this by increasing their bid after separating them from the rest. In turn we will lower the bids of the others.
3) Ranking highest all the time means you want to always be on Google top page, your quality score firstly needs to be good, at least above 6. Then even at that, you have to look at the competition, if they are as good as you, then the only way in to outbid them to boost your Adrank, cause as we know, Ad Rank = Quality score X Max CPC
4) remarkting needs to always be setup while targeting audiences that have almost completed an action and audiences that are similar to the ones that have fulfilled your marketing objectives
5) Display helps reduce cost, improves brand awareness and can generate leads