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Your questions:
Of course you can connect from your local network.
You can put any IP in your client config - public, private, whatever - as long as it is the correct ip to connect to your server! So if your client is in local network, you should put the private ip inside the client.conf, not the public one!
If you want your openvpn server to be available ...
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Here are a couple of techniques, which I used a lot for similar tasks.
you can use jump server for forwarding traffic between your raspberry PI and you (your ssh client), however, you should somehow manage to connect (using reverse ssh) your raspberry to the jump server. This can be achieved via cron jobs or using PubSub messaging (Amazon IoT, PubNub, etc.) ...
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