Fallacies are arguments that employ faulty reasoning. Given their persuasive and seemingly valid nature, fallacious arguments are often used in political debates. Employing these misleading arguments in politics can have detrimental consequences for society, since they can lead to inaccurate conclusions and invalid inferences from the public opinion and the policymakers. Automatically detecting and classifying fallacious arguments represents therefore a crucial challenge to limit the spread of misleading or manipulative claims and promote a more informed and healthier political discourse. Our contribution to address this challenging task is twofold. First, we extend the ElecDeb60To16 dataset of U.S. presidential debates annotated with fallacious arguments, by incorporating the most recent Trump-Biden presidential debate. We include updated token-level annotations, incorporating argumentative components (i.e., claims and premises), the relations between these components (i.e., support and attack), and six categories of fallacious arguments (i.e., Ad Hominem, Appeal to Authority, Appeal to Emotion, False Cause, Slippery Slope, and Slogans). Second, we perform the twofold task of fallacious argument detection and classification by defining neural network architectures based on Transformers models, combining text, argumentative features, and engineered features. Our results show the advantages of complementing transformer-generated text representations with non-text features.