Currently there's no way to extend a private contract to other parties (although this is on the Quorum/Tessera roadmap).
So at the moment, you would need to do it manually or within the contract itself by reading data from the old contract.
Provided you are using the same algorithm that ETH uses for your private chain, you will always have to mine in order to create blocks and process transactions.
Since it is a private blockchain, there should not be many miners on the network, and thus the hashing power should be low. Because of this, you are able to mine with a simple CPU and very little ...
There are a number of bridge services readily available for Ethereum, obviously the use will depend on your exact use case, but here are a selection of projects for you to review:
Parity Bridge: https://github.com/paritytech/parity-bridge
And here is a sample project of having 2 Quorum blockchains implementing a ...
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