for bitcoin core: simple answer is no, you don't need it.
But you need the rpc port to be exposed to the outside world to be able to comunicate with it over the internet.
If there is a wallet on the bincoin-qt/bitcoind this is a very bad idea!
Instead, if you want to connect two servers in a different location over the internet, then you have to use a vpn as best. You can use openvpn on both sides of the servers.
for your JSON-RPC client based on GuzzleHttp you need PHP.
But I would not recoment to use that, did you read that:
https://github.com/denpamusic/php-bitcoinrpc/issues/44Please provide the bitcoin.conf so that others can also learn from what you found.
Did you try to test the rpc over shh localy (on the server itself) to ensure this works?
It is essential that you have read and understand this:
https://en.bitcoin.it/wiki/API_reference_(JSON-RPC)