Is it permissible to greet in a language other than Arabic, despite being able to speak Arabic? And is it obligatory to return a greeting that is written or heard through media and the Internet, or is it merely recommended?

There is no objection to greeting someone in a language other than Arabic. If a letter containing a greeting arrives, it is obligatory to respond immediately with a verbal greeting, in accordance with the Almighty’s saying: "And when you are greeted with a greeting, greet [in return] with one better than it or return it [in kind]." Responding to a letter is not obligatory unless there is something that necessitates it. If a direct, comprehensive greeting is conveyed via radio, television, or the internet, everyone who hears it must respond. However, the obligation is lifted if someone else responds, as it is a collective obligation (fard kifayah). As for indirect transmission or a greeting addressed to specific individuals, a response is not obligatory.