Morse theory says that every Morse function $f$ (that is all critical points were non-degenerate and distinct critical points take distinct critical values) satisfies $$\#\min+\#\max-\#\mathrm{saddle}=\chi(M).$$ So, in the case of torus (that its Euler char is $0$), the functions must have $\#\mathrm{saddle}=\#\max+2$. By the fact that [all continuous functions on a compact domain attaint at least a max and a min][1] therefore we should have at least a max point then at least 3 saddle point for torus. in the case of sphere is similar. $\#\min+\#\max-\#\mathrm{saddle}=\chi(\Bbb S^2)=2$ so having two global minima we must have $\#\max=\#\mathrm{saddle}\neq 0$. In any case we have at least a saddle point. Note that these are non-degenerate critical points (that means Hessian is nonsingular at that points) and [there is a function on torus with 3 critical points](https://mathoverflow.net/q/229906/90655) i.e. a min, a max and a *degenerated* saddle point. [1]: https://math.stackexchange.com/q/109548/272127