1. Can you send an email from a web page using just HTML/CSS? She say yes, you can. When I asked her how she accomplishes this, she ignores me. She professes to do all her sites with just HTML/CSS, but my understanding is that to send an email you have to have some server side code to accomplish this task. I think she's using a plug-in of some type, probably Wordpress.
Yes and no - you can setup the fields to gather the information for the email (To, Subject, Body, etc.) using HTML, but something server side will need to process and send the email. A basic SMTP server is required at a minimum.
2. She states that you can put your content in any order you want in your HTML doc & then use CSS to place it correctly on the page. She states that for SEO, you should put all of your content at the top of your HTML doc & place your banner & navigation after the content. Then using CSS, you can place these items appropriately. I've tried this with several variations & my page was terribly skewed. I'm still fairly new at CSS, but my experience has been that it does make a difference where you place your div tags within your HTML doc.
She's technically correct - CSS is pretty flexible -
but, a web developer should worry first about building a page that displays itself quickly and efficiently to the user rather than about SEO. Many sites now are almost entirely dynamic, and the position of the content and navigation elements within the served page is built by a server side application and served to the user. I honestly haven't built a site in many years using plain HTML and CSS (like one would with Dreamweaver or another web dev application) - I still use CSS and HTML heavily to build content, but actually building a site (or even a single page) using HTML and CSS is largely impractical.