Does crying over one’s situation and feeling that it will not change prevent one from receiving the reward of the patient, or is it considered despair of God’s mercy or a lack of contentment with His decree?

Weeping at the time of calamity, without wailing or slapping, does not contradict patience nor does it indicate a lack of contentment with Allah's decree. Nor does it prevent one from receiving reward. The Prophet, peace and blessings be upon him, permitted this, just as Jacob, peace be upon him, wept over the loss of Joseph until his eyes turned white from grief. The mere shedding of tears and sadness of heart do not contradict patience, as long as they are not accompanied by discontent or despair.