All perfect praise be to Allah, The Lord of the worlds. I testify that there is none worthy of worship except Allah and that Muhammad is His slave and Messenger.
With regard to your first question, according to the scholars who held that a slight barrier (on the skin) is absolutely excused if it is hard to remove, such as Shaykh Ibn Taymiyyah, then we have not come across a statement of the Shaykh on the matter (of repeating the ablution or Ghusl when the barrier is removed).
Washing this spot in order to be on the safe side or repeating ablution, according to the opinion of those who held that continuation (i.e. continuation when performing ablution means not delaying the washing of one limb until the limb before it has dried) is one of the obligations (of ablution) in matters that are not difficult to do, is a good thing.
As for the view of the majority of scholars, who are not of the opinion that a spot is excused, then the ruling that applies to this spot is the same as that of a splint; one wipes over it (with a wet hand) when it is not possible to remove it. If it is removed after that, it is like the splint when it is removed – which is subject to the known difference of opinion among scholars. According to the majority of scholars, one repeats the ablution.
Shaykh Ibn 'Uthaymeen said:
“If there is a barrier that prevents water from reaching the skin, then it cannot be said that he washed the body part, but Shaykh Ibn Taymiyyah said that a slight barrier is exempted, especially if one is often afflicted with it. This applies to the workers who use paint; there is often a spot or two of paint, and they either forget to remove it or they do not find something by which they can remove it immediately. So according to the view of Shaykh Ibn Taymiyyah this is excused. However, we have to act according to the hadeeth narrated by ‘Umar ibn Al-Khattaab, which says that a person performed ablution and left a spot equal to the size of a fingernail (unwashed); the Prophet saw that and told him, ‘Go back and perform ablution well.’ The man went back (and performed ablution well) and offered the prayer. [Muslim] The hadeeth indicates that a barrier is not excused even if it is slight. So if he can remove it before the expiry of the time of the prayer, he should remove it. Otherwise, he wipes over it and it is considered like the splint.”
As regards your second question, it is not obligatory to remove the wax that is inside the ear, trim the mustache (or hair), or to cut the nails before Ghusl.
For more benefit, please refer to fatwa 289168.
Allah knows best.