Is it permissible to fast a voluntary fast with two intentions (making up a missed fast and a Sunnah fast)? And what is the ruling on fasting for the traveler and the sick person who are able to fast?

It is not permissible to fast voluntarily with two intentions (making up for missed fasts and performing a supererogatory fast). It is better for a traveler, who is eligible for the shortened prayer, and a sick person, who finds difficulty in fasting, to break their fast. It is obligatory for anyone who would be harmed by fasting to break their fast. They must make up the days they missed. However, their fasting, despite the hardship, is valid.