I am interested in a PhD program and would like to work with a particular advisor. He is 69 years old now, and I am wondering whether he will retire soon, but I am not sure whether this is not a bit rude to ask. What can I expect, generally speaking? Shall I email him and ask him directly?
By asking, "are you accepting PhD students in the coming academic year?" you will find out not only whether they are openly planning on retiring soon, but also critically whether their docket of students is full. You can do this via email without risking offending them. In your email, also justify why you are interested in working with them.
I personally have experience with this, and unfortunately the person I contacted was retiring in the next year, and they told me so when I emailed them.
Feel free to ask.
You might get a specific answer like "in 2 years" or "when my retirement condo is paid off", or they may not know.
They might want to keep going until they can't any longer. This is quite common.
Unless they say something like "at the end of this year", then work with them if they are willing to work with you.