Connecting a node to a hard-forked private network

Hey everyone, I've got some questions. I'm trying to hook up bitcoind to a local network that did a hard fork from Bitcoin. The peer's Bitcoin ports are all blocked from outside access, like 8333 and 8332. Any tips on how to set up the node under these conditions? By the way, I've got the ElectrumX server all set up and reachable, plus the nomp (node-open-mining-portal) is working too. Appreciate any help!

What exactly do you want to achieve? Since you mentioned "hard forked of Bitcoin" are you planning to fork Bitcoin and create an altcoin or do you just want your node accessible to the local network? If you want to access your node locally and bitcoind to accept JSON-RPC commands locally then you will need to configure your Bitcoin.conf file. Sample bitcoin config Read more from this link below to configure the network. - https://github.com/ElementsProject/elements/blob/master/share/examples/bitcoin.conf If this is for educational purposes better enable testnet.

There is private chain with nodes which are reachable only by the founders at the moment. But I’m looking for ways to start mining now cuz the mining cost is very low now. Is there a way to start mining in this case?

You would need to obtain permission and the necessary credentials from the founders to access the private chain. This may include VPN access, SSH keys, or other authentication methods depending on the network setup. Without that infos you shouldn't get your hopes up too high as things like the standard ports (8333) are blocked for a reason.

You need to communicate with the founders or administrators of the private blockchain network and work within the rules and permissions they have set. Or,  if you can become a node operator within the private blockchain network, you may have the ability to participate in the consensus process and mine blocks.

If the hardfork has changed the protocol's network data in a way that is incompatible with the one Bitcoin Core generates (and receives), then all interactions from such a network with the client will fail. That's why it's called a "hard fork". You should ask the coin developers how to connect to such a network.