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Yes, the RSK network is a public, permissionless peer-to-peer network. Anyone can run RSKj, the RSK node, if they are able to meet these (extremely minimal) hardware requirements: click here. To do so, follow the installation instructions available here for various systems/platforms. For developers, the RSK node is open source, https://github.com/rsksmart/rskj/ and you are free to build from source.
Yes, the RSK node is open source, https://github.com/rsksmart/rskj/, and anyone can make their own copy and modify it. The RSK community welcomes alternate implementations of the node software. Note that these alternative implementations do need to be compliant with the consensus rules in order to be part of the same network as the rest of the nodes - as is the case in any other blockchain network - and therefore any modifications should ensure that they are consensus compliant. Modifications to the consensus rules require RSKIPs.