Is it obligatory to make up seven years of prayers due to ignorance of the rulings of prayer, then abandoning them for a period, with no certainty as to the exact number of missed prayers?

If the prayers you did not perform well are invalid, then you must make them up. If you do not know their number, then estimate them and pray what you believe is sufficient to clear your conscience. Shaykh al-Islam Ibn Taymiyyah and some scholars hold the view that there is no obligation to make up prayers for someone who unknowingly omitted a condition or a pillar.