Now if I generate a private key on mainnet, can I use it on Ethereum Classic at the same address? What about testnets?
Yes, that’s exactly how it works – Ethereum, ETC and all testnets (Ropsten, Kovan, Rinkeby) generate the address from the private key in the same way. Also other Ethereum-based blockchains like Expanse or Ubiq.
You can confirm this on MEW by going to the View Wallet Info tab and trying the same (random, e.g. 0x0101…0101) private key while connected to different networks: the generated address is in any case same.
In what cases would the keys on different networks/chains not give the same address?
The address generation method is given in the Yellow Paper Appendix F. If the chain does not match, other addresses are generated.
A follow-up question would be: since provided contract addresses are derived from nonce and sender address, does this mean that if I provide n contracts on different networks and chains, the n contracts would have the same set of addresses on different networks?
Again, yes.
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