See, the nonce in Bitcoin is basically a number that miners keep changing to try to make the block comply with the network's rules. Think of the nonce range as searching for a specific combination on a lock, and that range goes from 0 to about 4 billion—pretty wide! When they run out of that range without finding anything valid, miners can change something else called the ExtraNonce, which expands the search possibilities. Ultimately, it's a process of trial and error. You don't calculate the nonce directly; you just keep trying until you find the number that works.

If you need to test your implementation on the Signet network, you can start by setting up your own Bitcoin Core node. It's reliable because you can control everything yourself. You just need to configure the configuration file and enable Signet. Now, if you prefer something faster, you can look into services like Blockstream. They're well-known and give you access to useful APIs, although you'd have to confirm whether they specifically support Signet.
To use the getblocktemplate and submitblock methods in Signet, you need to configure your Bitcoin Core node to connect to the network. With getblocktemplate, you're basically asking the node to give you all the information needed to create a new block. There are parameters like including rules to support SegWit, which is important for modern transactions. Then, with submitblock, you're sending that block you already created back to the node for it to accept and pass on to the network. The thing to keep in mind in Signet is that blocks have to be signed correctly, so you need to configure the parameters related to private keys and the special Signet challenge correctly for everything to work.