What does it mean to logically imply another predicate?
$F_1$ says for all $x$, there exists a y such that $P(x)$ implies $Q(y)$.

$F_2$ says for there exists a $x$, for all $y$ such that $P(x)$ implies $Q(y)$.

$F_3$ says that for all $x$, if $P(x)$ holds, then there exists a $y$ such that $Q(y)$.

$F_4$ says that there exists a $x$, such that if $P(x)$, then for all $y$, $Q(y)$ holds.

The first one means that for all values of $x$, there exists some value of y such that the $P(x)$ implies $Q(y)$. 

The second one says that there exists a common $x$ for all $y$ such that $P(x)$ implies $Q(y)$. 

Both of them aren't the same, which is what you have pointed out too and you can solve the rest of them in the same way.

Also, a good way would be to some concrete example and see if it holds or not. It makes the intuition a bit easier. 

EDIT: If you want more help with logical implications, there's a book called How To Prove It by Daniel Velleman whose first two chapters deal with logic, which is a good read.