What parameters are used to calculate the challenge string during bitcoin mining (blockchain creation)? How is the challenge string computed mathematically? What's preventing some node on the bitcoin network from broadcasting a challenge + proof to other nodes as it's own when it received it from some other node? 

A parallel to this question would be, how do a node, on receiving, the challenge + proof, authenticate the node which produced this combination?

I tried looking this up elsewhere, but the details of the challenge string calculation seems to be abstracted away in most tutorials.

Thanks in advance!
The data that is hashed, and the hash of which must be below the current target, is the block header. The block header consists of the block version number, the hash of the previous block, the Merkle root of the transactions in the block, the time, the target, and a nonce.

The generation of new bitcoins happens with a transaction, the first transaction of the block, which generates new bitcoins out of thin air. No part of the block can be changed without the hash changing and therefore becoming invalid, and that includes the coinbase transaction's output(s).