1. Because she will come here, I will meet her.

2. Because she comes here, I will meet her.

3. As she will come here, I will meet her.

4. As she comes here, I will meet her.

(Which one is grammatical?)

The first sounds like you both have a specific meeting planned, while the second seems like she habitually comes to the place, so you decide you will meet her there.

Both are better than the last two.

I hope this helps. Thanks for asking