Can both ends of a gRPC connection accept method calls?

What you can do is start a HTTP server in both processes and use clients at each end to initiate communication. There's a bit of boilerplate involved and you have to design a simple handshaking protocol (one end registers with the other, advertising its listen address) but it's not too much work.

The protocol does not implement it, but you may pretend this situation.

Define a server method that returns a stream of a ServerRequest message:

import "google/protobuf/any.proto";

service FullDuplex {
    rpc WaitRequests (google.protobuf.Any) returns (stream ServerRequest);
}

message ServerRequest {
    float someValue = 1;

    float anotherAnother = 1;
}

ServerRequest may be an Oneof, so your may receive different types of server requests.

If you need that your client sends back a response for each request, you may create a stream from your client to the server, but you will need to implement a logic in your server side that triggers a timeout waiting for that response.

service FullDuplex {
    rpc WaitRequests (stream ClientResponse) returns (stream ServerRequest);
}

No, a server cannot invoke calls on the client. gRPC works with HTTP, and HTTP has not had such semantics in the past.

There has been discussion as to various ways to achieve such a feature, but I'm unaware of any work having started or general agreement on a design. gRPC does support bidirectional streaming, which may get you some of what you need. With bidirectional streaming the client can respond to messages from server, but the client still calls the server and only one type of message can be sent for that call.