The correct statement(s) about the shapes and bonding of molecules and ions is(are)

Use VSEPR with lone pairs placed equatorially in a trigonal bipyramid. $\mathrm{SF_4}$ has 4 bond pairs and 1 lone pair; the lone pair sits in an equatorial position (fewer 90 degree repulsions), giving the see-saw shape, so (A) is wrong because of the axial claim. In $\mathrm{I_3^-}$ the central iodine has 2 bond pairs and 3 lone pairs, $sp^3d$, and the three lone pairs occupy the equatorial plane, leaving the three atoms linear; (B) is correct. $\mathrm{XeO_3}$ has 3 bond pairs and 1 lone pair on xenon, $sp^3$, so the molecule is trigonal pyramidal, not planar; (C) is wrong. $\mathrm{BrF_5}$ has 5 bond pairs and 1 lone pair (octahedral electron geometry), so the molecular geometry is square pyramidal; (D) is wrong.