Is it obligatory to remove dirt that is difficult to dislodge from cracks and prints on the sole of the foot before Wudu', and how frequently should one attempt to remove it if it takes a great deal of time and effort?

For the validity of ghusl (definition) (ritual bath) and wudu (ablution), it is a prerequisite to remove everything that prevents water from reaching the limb. Complete cleanliness is not a condition; the important thing is for water to reach the skin. Therefore, if the dirt does not prevent water from reaching the skin, its removal is not obligatory. Some scholars have made concessions regarding minor dirt that is difficult to remove, by analogy with the dirt under the fingernail. This is the choice of Ibn Taymiyyah, who extended it to include any minor impediment that prevents water from reaching any limb, due to the hardship involved, as Allah Almighty says: "And He has not placed upon you in the religion any difficulty" (Qur’an 22:78). So, if the dirt does not act as a barrier, or is minor, or its removal is impossible, or its removal is difficult, then wudu with it is valid. It is advised to avoid obsessive doubts (waswasah).