Add an item (to the end of the chain) O(1).
It depends on the implementation. Usually a classic LinkedList doesn't have a pointer to its last element, so It would be O(n). If we have a pointer to its last element, so yeah, it would be O(1).
Add an item (at some position in the chain) O(n).
Correct.
Find whether or not the chain is empty O(1).
Correct.
Check to see if the chain contains a given integer O(n).
Correct.
Get an item (i.e. the integer in the integer field) at some position in the chain O(n).
Correct.