When saving your project, select "Save as single file" to get a .capx. You have attached a .zip file of your project files.
The .capx is basically just an archive of your project (like .zip), but we can open it directly in C2 without having to extract the archive and cluttering our folders with a bunch of project files.
Now, on to the question:
The easiest way is if you use the bullet behaviour on your enemies, and when your character is within a certain distance (use the distance expression like squiddster said), rotate your enemy towards your player. (use the action "Rotate towards position")
Now, you have 8 animations for the enemy? You can compare the angle of the object to see which direction it's moving. If the angle is within 45 degrees of the angle 0 for example, the enemy is moving right. If within 45 degrees of the angle 45 degrees it's moving down-right, if within 45 degrees of the angle 90 degrees, moving down, etc..
Edit: And btw, the free edition only limits the amount of events and the amount of layers in each layout. All the features are available except for families.