How much data do you need to build a classifier?
It's impossible to answer this question in general, because the answer strongly depends on the content of the data. More precisely it depends if the relations between the features and the target class in the training data are sufficient for the parameters of the model to be estimated as accurately as possible. In the most simple cases a few instances might be enough, for example a linear regression model with one single feature would need only two &quot;perfect&quot; instances. Practically the following factors have a strong impact on the number of instances needed:

the number of parameters to estimate and the complexity of the model: a more fine-grained model needs more detailed information, i.e. more instances
the number of classes, because there are more possible combinations for the model to learn and because it usually implies a higher number of parameters as well (more complex model)
the number of features, for the same reason
the amount of noise in the data, because finding the general patterns is more difficult if there are lots of inconsistencies/errors in the data, so statistically more instances are needed to distinguish the effect of chance from the real patterns.

So the only way to check how much data is needed for a particular task and dataset is to do an ablation study, i.e. a series of experiments in which a model is trained every time with a different number of instances. For example if one has 1000 instances, they could try to train a model with 100, 200, 300,...,1000 instances. Then by plotting the performance of every model one can observe whether the curve becomes stable at some point: if yes, this point shows how many instances are needed. If not (i.e. the performance keeps increasing significantly), then more than 1000 instances are needed.

I think the size may affect the accuracy/precision of a classifier, but I am not sure 100% of that.

Definitely.