Does reinforcement learning require the help of other learning algorithms?
You do not need additional learning algorithms to perform reinforcement learning in simple systems where you can explore all states. For those, simple iterative Q-learning can do very well - as well as a variety of similar techniques, such as Temporal Difference, SARSA. All these can be used without neural networks, provided your problem is not too big (typically under a few million state/action pairs). 

The simplest form of Q-learning just stores and updates a table of &lt;state, action&gt; =&gt; &lt;estimated reward&gt; pairs. There is no deeper statistical model inside that. Q-learning relies on estimates of reward from this table in order to take an action and then updates it with a more refined estimate after each action. 

Q-learning and related techniques such as Temporal Difference are sometimes called model free. However, this does not refer to the absence of a statistical model such as a neural net. Instead, it means that you do not need to have a model of the system you are learning to optimise available, such as knowing all the probabilities of results and consequences of actions in a game. In model free RL, all learning can be done simply by experiencing the system as an agent (if you do have a model then it may still be used for simulation or planning). When considering whether or not you need a neural network, then the term tabular is used for systems that work with explicit value estimates for every possible state or state/action pair. And the term function approximation is used to describe how a neural network is used in the context of RL.

For large, complex problems, which may even have infinite possible states, it is not feasible to use tabular methods, and you need good generalised value estimates based on some function of the state. In those cases, you can use a neural network to create a function approximator, that can estimate the rewards from similar states to those already seen. The neural network replaces the function of the simple table in tabular Q-Learning. However, the neural network (or other supervised ML algorithm) does not perform the learning process by itself, you still need an "outer" RL method that explores states and actions in order to provide data for the NN to learn.