That got me thinking... with English heavily influencing Dutch, I would expect "he" to sneak in at some point, especially in the informal spoken and written communication of young people. Is it happening?
No, I've never heard some one use 'he' for 'hij'. Though the influence of English is seen in comparisons. The correct way of saying 'You're better than me' in Dutch is 'Jij bent beter dan ik'. But due to English having a great influence on Dutch, some people would rather say 'Jij bent beter dan mij', using 'mij/me' instead of 'ik' because it looks more like the pronoun you'd use in English.
No, they are all conjugations of the verb zwemmen (swim) in the present.
U zwemt (formal you)
Hope this helps.