I think both are false.

For 1st, It will be O(EV) because the decrease-key operation will take O(n) times and we have to perform that operation E times.

For 2nd, Kruskal's algorithm is **always** disconnected. Here always word makes it false, we can intentionally create such a graph where kruskal's MST is also connected.

For example: 1 ---> 2 ---> 3 ---> 4

(1) (2) (3)