Is it permissible for a man to travel and leave his wife in a foreign land to marry another, or to perform Umrah or Hajj, when there are trustworthy non-mahram friends who reassure him about his family? And what are the conditions for a man to leave his wife and travel for any reason?

There is no objection to a husband traveling and leaving his wife in her city if he is sure of her safety. It is not a condition for her to have a mahram (definition) with her, as a mahram is required for a woman when traveling, not when residing. The important thing is that she is safe.