You have one variable with three groups.I have three independent variables (2 treatment & 1 control)

test scores are not variable. They're measures of variables. What does the test measure. That's your variable.1 dependent variable (a test score).

Here you kinda lost me. What you do witht he anova is see if there are any differences in the three groups with regard to 'test score'. If there is you want to know whare. This is where you may use J-1 post-hoc comparisons between groups (basically a t-test) where J is the number of groups you have (so for you: you can do 3-1 =2 comparisons).After I collect my data, I would like to conduct a test that looks to see if there is any significance between low and high performers (50% split) based upon the test score. So here are my questions:

1. Is comparing based upon the two groups appropriate?

2. Is this properly called a split-wise comparison?

3. Would the placement in low/high gropuing be a dependent or independent variable?

As a side note if you have a theory about directionality you may want to forgo the anova and use a planned contrast instead. this increases power but you'd better be sure about directionality of the differences. So, in general, the anova is less powerful than the planned contrast but safer.

I'm a little confused about your design so there may be a better asnwer for what you are planning. If you gave your research questions this would provide more information to help you.