And "The website should be accessible to search engineer spiders and be coded with good on-page search engine optimization." is a pretty squishy requirement. It's like saying "the pages must load quickly".
You may wish to seek clarity from your project manager.
Sometimes, the SEO aspects of a web site are controlled by the Marketing Department. If so, they will often have a set of keywords they expect potential customers will use. And they will often have a set of reports that they wish to receive from the system (indiating hits, page loads, referrers, etc).
Yeah, there are tons of rules for testing SEO of a page. Marketers should know, but some basics are 1) Key words should be defined in the HEAD information, 2) There should not be excessive use of any given word in the keywords, 3) A Definition should be defined in the HEAD information, 4) first few paragraphs on the page are descriptive and content-rich (tell what the page is about), 5) last couple paragraphs are content-rich (winding down, but still containing keywords or phrases), 6) Important one, the page should contain all keywords within the context of the page, or face possibile penalties by the search engines in the rankings.
Here are a few points to test for website SEO:
1. URL (Directory Structure) - Avoid long URLs
2. Title and Meta Tags Optimization against keywords
3. Alt Tag Optimization
4. Google sitemap.xml creation and submission
5. Robots.txt file and its proper use
6. Proper keyword saturation on every page
7. Number of outgoing and incoming links on each and every page
8. Anchor text Optimization
These are some points that need to be tested for your site and numerous others to cover. It would be better to start reading a few articles on SEO and its methodology.
9. Use Text instead of Icons (Icons can't be read by search engines)
10. Use "speaking" URLs (e.g. www.testforSEO.com instead of www.somecrypticletternumbercombination.com)
11. use your specific keywords (the ones you want your website to be found under) in Headings
12.web pages should load fast (fast pages preferred by search engines)