Can a salafi student of knowledge in the west who learnt arabic, was at the dawraat of the 'ulama and has contact with them teach publicly salafi books with the 1:1 translation from shaykh fawzan uthaymeen etc. Without a direct tezkiyyah or diploma of a faculty?

Ustadh AbdulAziz al-Haqqan

Yes if his sheikhs allowed him to do so.