Is it true that every Muslim must enter Hellfire before Paradise, except for the prophets and martyrs, and is this statement despairing of God's mercy?

This statement is incorrect. Among Allah's servants are those who are neither prophets nor martyrs, yet they will enter Paradise without torment or reckoning. As it is mentioned in the noble Hadith, seventy thousand from this Ummah will enter Paradise without reckoning or torment. Ibn Abbas and Ibn Mas'ud stated that among the Ummah of Muhammad, peace and blessings be upon him, there are forerunners who will enter Paradise without reckoning, moderates who will be given an easy reckoning, and wrongdoers who will either be forgiven or enter Paradise by Allah's mercy after having committed grave sins, provided they did not associate partners with Him. As for despairing of Allah's mercy, it means losing hope in it.