Was prayer forbidden in the camels' resting places, while the Prophet (peace and blessings of Allah be upon him) built the Quba Mosque at the resting place of his she-camel? Is the latter narration authentic, and how do we reconcile between them if it is?

The Prophet's Mosque was built at the resting place of the Prophet's camel in Medina. This spot was originally a date-drying ground belonging to two orphan boys, and the Prophet purchased it from them.

There is a prohibition against praying in camel resting places (mabārik al-ibil). This refers to their habitual enclosures, not every place where a camel might temporarily kneel. The kneeling of the Prophet's camel was incidental and does not fall under the category of 'ma'āṭin' (camel enclosures) where prayer is prohibited.

Even if we assume it fell under the prohibition, the construction of the mosque on that site removed its characteristic of being a "camel resting place." This is similar to the Prophet's Mosque itself, which was originally a cemetery for polytheists before the land was leveled and the graves removed. The legal ruling ceases when the characteristic to which it is attached no longer exists.