When applying for eTA, the signature part says to sign, enter your name as it appears on your passport. Does that mean I just write my full name and not actually my signature? Also do I have to do it in capitals?
Yes. There is a help document available to guide you through the eTA application process (accessible in various languages from here). On page 19 of the english document, it clarifies that you should enter the full name, not just an abbreviated signature you would sign with pen and paper.
I am not sure whether capitalization is actually relevant, but for what it's worth, I did use capital letters only (because that is how it actually appears in the passport) and it seemed to be ok.