Why be formed face to split when apply the Solidify modifier? I'll make the modeling by two axis Mirror modifier. But, when, apply Solidify modifier, Its has be formed face split at meeting point vertex of the Mirror modifier.

Show you next pictures:
 - When apply the modifier not yet:




When apply the modifier:




Q. How to remove the faces?



blender_2.81
You need to enable the "Clipping" option in the mirror modifier. If you don't, the two halves of the model are treated as if they're disconnected at the seam in the middle.