Step 1: Let's analyze the statements:
Option (A) BeO indeed has a rock-salt structure, so statement i is correct.
Option (B) BeSO\(_4\) is actually poorly soluble in water, so statement ii is incorrect.
Option (C) The maximum coordination number of beryllium is 6, not 4, so statement iii is incorrect.
Option (D) Be(OH)\(_2\) is basic in nature, which is true, so statement iv is correct.
Thus, the incorrect statements are ii, iii, and iv. Therefore, the correct answer is option (2).