In an SVM, does a more negative/positive decision score mean that it is further from the seperating hyperplane? For example, if I have a sample with a decision score of -6 and another  with a score of -3, which sample is closer to the hyperplane?

Also, does the probability of a sample belonging to a class increase with its respective distance from the hyperplane (larger distance from hyperplane = larger probability)?

I am using sklearn's decision_function and predict_proba functions to get these values if it makes a difference. 

Thanks.
Larger scores do mean farther from the separating hyperplane.

The SVM model itself isn't modeling probability, so you can't quite say that farther points are considered more probably in one class or the other by the model. There are ways to estimate a probability (see the scikit implementation) for example and yes it will generally be true if so that farther points are more certain, according to that estimate.