As far as I remember, terminal state is a state from which agent cannot escape, i.e if the agent reached this state, he will never escape. In mathematical notation can be written as: $$ p(s^{'}, r|s_T,a) = \delta_{s^{'}s_T} \delta_{rr_{S_T}} $$ Where $\delta_{ab}$ is a Kronecker symbol, and by $r_{S_T}$ i mean the reward collected by the agent sitting in the terminal state from now till the end of the episode.

This state doesn't have to be unique. Imagine a Markov chain as a set of points, representating states and arrows between the states with associated probabilities. Nothing prevents you from defining MDP, where several nodes have only one outgoing arrow pointing to itself with the probability 1.

As far as I remember, terminal state is a state from which agent cannot escape, i.e if the agent reached this state, he will never escape. In mathematical notation can be written as: $$ p(s^{'}, r|s_T,a) = \delta_{s^{'}s_T} \delta_{rr_{S_T}} $$ Where $\delta_{ab}$ is a Kronecker symbol, and by $r_{S_T}$ I mean the reward collected by the agent sitting in the terminal state from now till the end of the episode.

This state doesn't have to be unique. Imagine a Markov chain as a set of points, representing states, and arrows between the states with associated probabilities. Nothing prevents you from defining MDP where several nodes have only one outgoing arrow pointing to itself with the probability 1.