1) There are 4 Bell states, namely the ones you listed divided by $\sqrt{2}$. There is no "the bell state". The Bell states are only defined for 2 qubits, so there is no "higher dimensional definition of a Bell state". One of the key features of the Bell states is that they're maximally entangled. If this is what you'd like in a higher dimensional analog of the Bell states then you'll want the GHZ states as Mark S suggests. An analysis coming to this conclusion can be found here: https://arxiv.org/pdf/quant-ph/9804045
2) The code space for the toric code on a 3x3 lattice consists of 4 different, long, complex superpositions of kets which each have 18 elements in them. I doubt anyone is willing to write them out for you. However it wouldn't be too difficult for a computer algebra system to crunch them.
Beyond being discussed in entry level texts for clarity, the actual codespace of an error correcting code is rarely ever used. The codespace is uniquely determined as the mutual +1 eigenspace of the code's stabilizers. In fact the stabilizers encode everything about the code so it's common to think of them as the code itself. Compared to the codespace, the stabilizers are much cleaner, more concise and obey nice algebraic properties which makes them preferable to use.
For the toric code the stabilizers are strings of $X$ and $ I$ or $Z$ and $I$ derived from the topology of a torus. It would be a tedious but straight forward exercise to explicitly enumerate all the stabilizers for the 3x3 lattice then find the elements spanning their mutual +1 eigenspace (hint: there's 4 of them encoding $|00\rangle$, $|01\rangle$, $|10\rangle$ and $|11\rangle$)
