Is a wife who died of a pulmonary embolism after a difficult birth and organ hemorrhage considered a martyr? And is it forbidden to wish for death in order to meet one's wife in Paradise?

Your wife is among the martyrs of the Hereafter, Allah willing. Wishing for death is disliked, but there is no harm in supplicating to Allah to reunite you with her in Paradise. You must be patient and submit to Allah's will, increase your prayers for your wife for forgiveness and mercy, give charity on her behalf, and any act of devotion whose reward you dedicate to her will benefit her.