Are these two totally synonymous? Can one be used in place of the other anywhere? Are there any differences in nuance, or anything at all?
These two are not equivalent. Even though is used to introduce a condition which currently is true, while even if introduces a hypothetical condition that is not yet true.
I'm going to the park even though it's raining.
This means that it's raining right now, but I'm going to the park anyway.
I'm going to the park even if it's raining.
This means that it's not yet raining, but I will go to the park even if it starts to rain. Note that in this case the present progressive I'm going actually indicates a near future action.