Is a son considered undutiful if he lives abroad for work while communicating with his parents by phone, given that his father is elderly and has no one to serve him? And is a father considered reproachful when he reminds his children of what he did for them?

If the father needs his son to stay with him and is harmed by his travel, then it is not permissible for the son to travel for work except with his permission. However, if the father is not harmed by his travel, then there is no objection to traveling for work even without the father's permission, and it is better to please him.

Boasting about good deeds is forbidden and invalidates the act, unless the doer of good is met with ill-treatment, in which case it is permissible for him to enumerate his good deeds. So, if the father mentions his good deeds due to his children's ill-treatment, he is not considered to be boasting.