Option 1 :- Every minimum spanning tree of G must contain $e_{min}$.
Kruskal's algorithm always picks the edges in ascending order of their weights while constructing a MST of G. So yes , it is true.
Option 2 : - If $e_{max}$ is in a minimum spanning tree, then its removal must disconnect G .
$e_{max}$ would be included in MST if and only if , $e_{max}$ is a bridge between two connected components , removal of which will surely disconnect the graph.
Option 3 :- No minimum spanning tree contains $e_{max}$.
Contradictory statement , already proved in option 2 that $e_{max}$ can be in MST. Thus option 3 is false.
Option 4 :- $G$ has a unique minimum spanning tree.
G has unique edge weights , so MST will be unique . In case if edge weights were repeating , there could've been a possibility of non-unique MSTs.
Thus it is true.