SVM hyperplane equations for linearly seperable data
Normalized / standardized data are necessary to train an SVM classifier. Before running an SVM you should always scale your variables: it can be done either through min-max scaling or with standardization (in statistics are called Z-scores).

It's a fundamental dataprep operation, without it a classifier such as SVM wouldn't be useful. That is because if variables are not on the same scale the ones with the larger variance will dominate all the others in the training.

The equations that you quoted are the support vectors. In the image next to them: the dashed lines whose distance must be maximixed by the SVM classifier. The values of 1 and -1 are the labels that the model is attributing to the target classes (in a binary classification problem).

Hope this helps, otherwise let me know.