Proper way to facilitate MOVE operation when overriding operator on C++

I'm not really familiar with how move works in C++, and I need some help to clarify my understanding. I'm want to overload the operator+, and I'm have a couple of questions about it.

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ap_n operator+(const ap_n& n, const ap_n& m) {
    ap_n tmp {n};
    return tmp += m;
}

My first question is how to make temporary objects movable. As shown in my function above, both arguments are not meant to be mutated, therefore I need to create a third object to do the operation upon.

How can I make my return value usable for move operation. Is the return value supposed to be a reference as ap_n&? Should the return object be encapsulated by std::move(tmp)? Or is it alright as is?

How does C++ decide when an object is rvalue, or decide that a move operation is suitable on an object, and how can I tell the program that an object is safe to use for move operation.

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ap_n operator+(const ap_n&, const ap_n&); // defined as in first question
ap_n operator+(ap_n&& n, const ap_n& m) { return n += m; }
ap_n operator+(const ap_n& n, ap_n&& m) { return m += n; }
ap_n operator+(ap_n&& n, ap_n&& m) { return n += m; }

My second question is whether it is necessary to create variants of function that accept rvalue arguments. Right now I have 4 functions, as shown, to be able to accept normal objects and rvalue objects.

Is writing all the combinations possible like this necessary? If I remove all but the first function, would the program still be able to perform move operation correctly?