Hi there.
I don't think there is any specific courses for technical SEO, since it includes html, css, js, jquery, php and more.
I think you would be better off trying to find lessons/guides for specific programming languages your website is built on, rather than trying to learn everything at the same time.
As for APIs - the same thing - there are lots of good tutorials for specific APIs, but to use them you need to know some of programming languages, since all APIs are based on one or another programming language.
So, my advice - find out which languages your website is built on, what API it uses and what language that APIs is operating with (most likely it will be the same as your website platform language), then find some crash course online for that language, spend couple weeks learning it - then you should be able to do simple technical SEO changes.
Hope this helps.