prediction for a linear sum
If it's exactly zero, you might classify it in either class. When using floating point numbers, there's a nearly 0% probability that an observation would ever have a predicted value of exactly zero. There's always some chance that observations will get the wrong label - that's how statistical models work, if you can find some rule that will with 100% certainty give you the right result, you shouldn't be using a statistical model in the first place.

I'm not sure why you want to "label test data". Test data is by definition labeled data that you set apart in order to get a hopefully unbiased evaluation of your model performance. Perhaps you mean making new predictions?