Is a qutrit an example of tripartite entanglement? Is a qutrit considered to be in a state of tripartite entanglement?
 A: 
Is a qutrit considered to be in a state of tripartite entanglement?

A qutrit is a (single) quantum system. As such, it may be isolated, or it may be interacting with one or more other systems, and it may (or may not) be entangled with those other systems, depending on the situation.
In other words, it is certainly possible to bring in two other systems (which may be qutrits, qubits, qudits, or anything else) and place the trio of systems in tripartite entanglement. But the fact that you have a qutrit, by itself, says nothing about whether it is entangled or not, or what the nature of that entanglement is.
The "tri" in "qutrit", in particular, has nothing to do with the "tri" in "tripartite".

*

*The "tri" in "qutrit" counts the number of states in the Hilbert space of the qutrit, i.e. the fact that there are three orthogonal states $|1⟩$, $|2⟩$ and $|3⟩$, that the system's state can occupy.

*The "tri" in "tripartite" counts the number of systems that go into the tensor-product state in which entanglement takes place, i.e. the fact that in a state like
$$
|\psi⟩ = |1⟩\otimes|1⟩\otimes|1⟩ + |2⟩\otimes|2⟩\otimes|2⟩
$$
there are three tensor-product factors in each of the components of the superposition.

