Yes, but keyword density should not be an issue today unless you are doing a ton of keyword stuffing. Anything you write should be natural for the website visitor. You can include semantic phrases that relate to the phrase that you are trying to rank for. In fact, I have seen evidence of a page ranking for a certain keyword phrase when that particular keyword phrase was not even mentioned once on the page!
For alt tags, anything you put in there has to describe the image itself. Anything else would be considered spam. Alt tags are used for screen readers for the blind so that the blind know that the image is about. If you have an image with text in it then put that text in the alt tag. If you have an image of a pie chart then describe what the pie chart represents.
You can use the HTML code ‘desc’ to add a longer text version of what the image is about that will help you with what you want to do. WordPress makes this easy by showing you a box to add text for a description for every image you upload to it. I have found that using the description box in WordPress really helped with product rankings.