Hi MAX WSD. Welcome to the forums.
You definitely need to be concerned—at least about the book. That's a terrible use of a table—utterly unwarranted. It's hard to believe a new book could even suggest such a thing. :rolleyes:
And if I use text images in my nav bar, won't that affect accessibility and hurt my seo? I thought the google font library solved small font issues across browsers.
Whenever you put text in images, you should use a text fallback—so it's not necessarily an SEO / accessibility issue if you do it right. Tables makes it harder, though. And yes, @font-face is well supported now, so this is another reason not to use that book.
Should I just go through the motions to complete the course and learn or understand the "right" way to do it on my own. Will I pick up too many bad habits?
Only you can answer that ... but first impressions are powerful, so be careful. The course organizers should be taken to taks for using such a questionable resource*, though. (Educational institutions have a pretty bad reputation for living in the dark ages ... and it's not hard to see why.)
[* OK, I guess I shouldn't judge a whole book on one issue, but really, it's not a book I could recommend now, knowing about that. I've had a "look inside" on Amazon, and it certainly is a big book with a lot of information, so I guess they chose it because it covers so much. It would be a good exercise to cross reference every topic with online resources, like the SitePoint HTML/CSS reference, to get some perspecitive on all this. And of course, feel free to run things past these forums, too!]