How can one respond to someone who uses phrases such as: "May God take you, may God uproot you, may God fail you," using God's name, or to someone who says: "May God curse your devil"?

It is not permissible to invoke curses upon others unless they are oppressors. If someone curses you, you may retaliate in kind, but forgiveness and pardon are preferable. As for cursing Satan, it is established in the Quran and Sunnah, but it is prohibited in certain contexts, such as when an animal stumbles, because it creates the illusion that Satan is the true perpetrator, whereas the act is from Allah. This also makes Satan gloat. However, there is no harm in using Allah's name with actions like "may He take you, may He uproot you, may He cause you to fail" in supplication, if the supplication is just.