Is it written anywhere in the Torah or the Mishna that Jews may not travel/live in Egypt? If yes then why are there Jews still there?

See Rambam Hilchot Melachim 5:7 "Living anywhere is allowed, except Egypt... the Torah has warned not to return to Egypt in three places..." etc. One of the commentaries ibid says it is allowed to return for business etc. Regarding the second question, we're not the ones to ask - you should ask the jews who live there. Rabbi Ro'i Margalit