Statement I  Shape of NF₃ and H₃O⁺ is same

Statement II Shape of isoelectronic species  is always same 

The species which have similar chemical structures are known as isostructural chemical compounds.

Considering $\mathrm{N}{\mathrm{F}}_3:$N has five valence electrons. In the given compound nitrogen is forming three bonds with fluorine atoms. Thus, nitrogen has three bond pairs and one lone pair. Its hybridization is $s{p}^3$ and the shape is pyramidal.

Considering $H_3{O}^{+}$ : O has six valence electrons. It forms two covalent bonds with two hydrogen atoms and a coordinate bond with the third hydrogen. In total, it has three bond pairs and a lone pair. The hybridization is $s{p}^3$ and the shape is pyramidal.

Statement I is correct.

${\mathrm{NH}}_3 \mathrm{and} {\mathrm{NH}}_2^{-}$ have same number of electrons (10), NH₃ have pyramidal shape whereas ${\mathrm{NH}}_2^{-}$has bent shape.

Statement II is incorrect.