- I will see the girl that is walking.
Is walking now? Yes
can it be simultaneous with seeing? Not as written. You would need to write I will see the girl that will be walking to make it simultaneous with seeing. Also acceptable is I will be seeing the girl that will be walking. The first implies that you will see her for some brief part of her walk, and the second implies that you will see her for a larger portion of her walk - perhaps if she's walking in a stadium around a track and you're sitting in the bleachers you can easily observe her entire walk, for instance. You probably want to avoid I will be seeing the girl that will walk because, unless you're dating her, it starts to sound creepy - it implies that you will be observing her for a period longer than her walk.
- I will see the girl that will walk.
Is walking later than seeing, or can it be either later than seeing or later than now? In this sentence, walking is later than now, and seeing is later than now. A listener might assume that these two events are likely to occur together, but there's no requirement that they occur together to make this statement. One could, for instance, plan to see the girl in 5 minutes and she will walk in 3 days, or else see the girl in 3 days and she will walk in 5 minutes, and in both cases the sentence above is acceptable. If you want to be clear that they will occur simultaneously then I already gave you that sentence above. If you want to be clear that she will walk, and then you will see her, you can say I will see the girl that will have walked. If you want to be clear that you will see her and then she will walk, you can say I will have seen the girl that will walk.
- I will see the girl that walked.
Is walking only before now, or can it also be before seeing which is in the future? Walking is only before now. If you want walking to be before seeing in the future, use the sentence I gave you above: I will see the girl that will have walked.