Is it valid to perform ablution by wiping the outer part of the ear and sufficing with that, and is it valid to perform ghusl by placing cotton in the ear for someone harmed by water?

Wiping the ears during ablution (wudu') is considered sunnah (recommended) by the majority of scholars, and the ablution is valid whether you wipe them or not. It is from the Sunnah to wipe them as long as it does not cause harm.

As for ritual bathing (ghusl), it is obligatory to wash the outer part of the ear canal (samakh) but not its inner part. If you are harmed by water entering it, you should place a patch over it and wipe over the patch, and do not remove it until you have prayed. If you wipe over the cotton and do not remove it until you finish the prayer, then your ritual purity (tahara) and prayer are valid. But if you remove it before the prayer, your ritual purity becomes invalid upon its removal. Some scholars are of the view that purity is not invalidated by removing what was wiped over.

If you do not wipe over the cotton, then your ghusl is not valid.

You are required to make up the prayers for neglecting purity due to ignorance, according to the majority of scholars. However, some, like Ibn Taymiyyah, are of the opinion that no make-up is required.