Is it permissible to stand up in a show of respect for someone, or to stand to greet him? And does one who is seated greet one who is approaching while remaining seated?

There is no harm in standing for an arriving person, as it is among the noble morals if the purpose is kindness, righteousness, and honor. The Prophet (peace be upon him) stood for Fatimah, and she stood for him. The Companions stood for Sa'd ibn Mu'adh, and Talhah stood for Ka'b ibn Malik. As for standing out of glorification, or standing while people are seated out of glorification, or standing upon entering without meeting or shaking hands, this is not appropriate. Even worse is standing to glorify someone who is seated.