If I train a model using only my testing data, will the accuracy be 100%?
It will likely be not 100% even though it is possible. But, for example, a linear model might not be able to represent a non-linear relationship in your data. Or your features don't contain sufficient information to separate all classes. 

Your other question doesn't seem to make sense. If you train your model on the test data, the test data wouldn't really be test data anymore?! 

There are tons of resources on bias-variance trade-off and overfitting.