Hi is it possible for me to visit the Canadian Embassy in Los Angeles, US, to apply for a F-1 Visa or do I must go back to my home country Canada and apply at the Canadian Embassy?
If you are a Canadian citizen, you do not need an F-1 visa. Once you have your I-20, depart the US and re-enter showing your I-20. If everything is in order, you will be given an F-1 based I-94 at the POE.
Is it possible to still get that done just by having an I-20 form or do I have to apply for a visa in the US Embassy in Canada?
Re-enter showing your I-20. Canadian citizens do not need an F-1 sticker on their passports.
OP, you haven't answered one basic question - are you a Canadian?