How can Achilles and Astolfo lend Noble Phantasm?
In actual legends, Achilles is known for giving away relics (e.g. For Patroclus to impersonate him, lending him his chariot and armor), and Astolfo is known for receiving them in his legend (which is why he has so many different Noble Phantasms, which he collected through his adventures). These circumstances allow the two to transfer and recieve other Noble Phantasm, which would not normally be possible (although there are exceptions, such as Berserker from Fate/Zero).

The anime itself is a poor adaptation, and glosses over or outright changes a lot of context and background information. Therefore a lot of thing the audience should know are left out arbitrarily.