Is it necessary to read "Al-Uddah fi Sharh Al-Umdah" or listen to its explanations, or is it sufficient to rely on books of fiqh and their explanations, especially since "Umdat Al-Ahkam" is a book of fiqh?

You have done well in memorizing the Forty Hadiths of An-Nawawi, and it would be excellent if you followed it up by reading the commentary of Ibn Rajab or An-Nawawi. You have also done well in starting to memorize the hadiths of 'Umdat al-Ahkam by Al-Hafiz 'Abd al-Ghani al-Maqdisi.

If you have access to tapes of Shaykh Al-'Uthaymin's commentary on Zad Al-Mustaqni', then begin studying Zad Al-Mustaqni' directly. Otherwise, start with 'Umdah, then Zad Al-Mustaqni'. The best printed commentaries on Zad Al-Mustaqni' is Ar-Rawd Al-Murbi' by Al-Buhuti.

One resorts to acquiring knowledge from scholars' tapes when there is no scholar available to sit with and receive knowledge from directly. This is because among the benefits of scholars' circles is that the student acquires from the scholar good manners, guidance, and noble character along with knowledge.