I was asked by my boss to 'have them arrange to do this' (where "them" is an external client) - I felt like this not the nicest form to ask an employee to do something, but I'm not native English speaker. What are your thoughts on this? Is such a form rude or completely normal?
This appears to be a perfectly normal form of language. It might be considered rather abrupt, and 'please have them arrange to do this' would be slightly politer, but it is not rude, with or without the please. The context and tone of voice used might modify how you perceive it, but that is independent of the phrasing.