Like fire hardened here is a simile for the bare red road, which in other words has the appearance of fire, if fire were somehow hardened into a surface. As you surmise, hardened here functions as an adjective modifying fire. The clause could alternatively have been written
It streaked beneath him like hardened fire …
It streaked beneath him, like fire hardened, …
In the second clause, does is an auxiliary. It inverts positions with the subject when it is paired with only and a subordinate clause that restricts the main action to certain conditions. This word order emphasizes the restriction:
Only when we believe do we understand.
Only after the rains fall do the flowers bloom.
But if we change the order of the sentence to put the main action first, we would not use do at all:
We understand only when we believe.
The flowers bloom only after the rains fall.