Your answers to $(1)$ are just fine. You seem to understand the relationships between an implication, its converse, inverse, and its contrapositive.
Implication: $A \equiv (p \rightarrow q)$
- converse of $A$: $\;q\rightarrow p$
- inverse of $A$: $\;\lnot p \rightarrow \lnot q$
- contrapositive: $\;\lnot q \rightarrow \lnot p$
Note that $\,A \equiv \text{contrapositive(A)}\;$ and $\;\text{inverse(A)}\equiv \text{converse(A)}$.
$(2)$ Here, your initial translation is incorrect, and as a consequence, so are the converse, inverse, and contrapositives.
Let's look at $(2)$ again.
Stop, or I'll shoot $\iff$ If you don't stop, then I'll shoot.
This can be translated into two equivalent logical statements:
$\text{Stop} \lor \text{Shot}\,\equiv \lnot \,\text{Stop}\rightarrow \text{Shot}\tag{2}$
Now, use what you know about the converse of an implication, the inverse, and the contrapositive to write the corresponding statements to the implication given on the right-hand side of $(2)$
UPDATE: Now you're spot on!
Close. The converse and contrapositive are off. The original statement is not a biconditional statement (those are of the form "X if and only if Y"). You could rewrite any conditional of the form "X only if Y" equivalently as "if X, then Y", that is, $X \rightarrow Y$.
Original statement ($X \rightarrow Y$): "We’ll win the ICG cup only if we have enough players". This is the same as saying, "If we'll win the ICG cup, then we have enough players." In this example X="we'll win the ICG cup" and Y="we have enough players". Plug in the values for your converse/inverse/contrapositive definitions to get the following.
Converse ($Y \rightarrow X$): "We have enough players only if we win the ICG cup." It is equivalent to say, "If we have enough players, then we'll win the ICG cup."
Contrapositive ($\neg Y \rightarrow \neg X$): "We don't have enough players only if we don't win the ICG cup." This is equivalent to saying "If we don't have enough players, then we won't win the ICG cup."
Inverse ($\neg X \rightarrow \neg Y$): "We won't win the ICG cup only if we don't have enough players". Equivalently you could say "If we won't win the ICG cup, then we don't have enough players."
Best Answer
Recall,
Statement: if $p$ then $q.$
Converse: if $q$ then $p.$
Inverse: if not $p$ then not $q.$
Contrapositive: if not $q$ then not $p.$
So, yes, your answers are indeed correct.