Is the remembrance of Allah and supplicating to Him accepted from one who has to make up old missed prayers, especially if he is making up one or two of them daily?

What you did not perform of prayers due to ignorance is considered a missed prayer (fawait) and must be made up according to the majority of scholars. However, it is permissible to follow the opinion of Ibn Taymiyyah, who held that there is no obligation to make them up. Whoever has missed prayers must make them up at any time, provided it does not cause harm. One should continue to make them up if the number is known; otherwise, one should make up what is most likely sufficient. Performing good deeds is not precluded by the presence of missed prayers.