Must all acts of worship that were performed (such as Wudu, Ghusl, fasting, and prayer) be repeated due to the presence of a transparent adhesive residue on the nail that was only noticed recently?

If the adhesive mentioned does not prevent water from reaching the skin, then it does not affect the validity of ablution (wudu), ritual bath (ghusl), or prayer (salat). However, if it does prevent water from reaching the skin, but covers only a small area of the nail, then it falls under the category of a slight barrier concerning which some scholars have been lenient. This is the chosen opinion of Sheikh al-Islam Ibn Taymiyyah, and there is no need to repeat previous prayers. As for fasting, it remains valid and has no connection to the adhesive.