Is it necessary to perform ghusl again if a small trace of semen is found after the first ghusl, or is that considered part of the initial semen? And is it necessary to do anything if a Muslim does not remember whether they conveyed water to between the buttocks during ghusl or not, after having been unaware of the obligation to do so?

If you find traces of semen after performing ghusl, it is presumed to have been discharged during the last sleep prior to its discovery, and you must perform ghusl again. You must also repeat the prayers you performed after your last sleep.

Al-Suyuti said: The principle for every new occurrence is to attribute it to the nearest time. And whoever sees semen on his clothes but does not recall a wet dream, ghusl becomes obligatory upon him, and he must repeat the prayers from the last sleep he had.

Al-Dasuqi said: If one sees semen on his sleepwear and does not recall a wet dream, and does not know when it occurred, ghusl becomes obligatory upon him, and he must repeat the prayers from the last sleep he had, whether the semen is fresh or dry.

As for doubt regarding water reaching a specific area after completing an act of worship, it does not affect it, and your prayers are valid. The strong presumption of water reaching the area is sufficient.