What is the meaning of this Links? In a big project how to find out whether a property has links or not. I assume a link is created after copy and paste.
This is a great feature that allows you to connect any property of a layer or an effect to another via expressions. One simple example is if you apply an effect to one layer but you want the same settings on multiple layers, you can select the effect, go to Edit > Copy With Property Links, then paste the effect anywhere in your project. You'll notice that the pasted effect has expressions linking each parameter back to the original instance you copied from.
A great practical use of this technique is to do the above, but on a null layer. Say you're working with drop shadows and you want to apply the same settings on 10 different layers. Instead of having your main drop shadow on one of your ten identical layers that you might lose track of later, you create a Null Object at the top of your layer stack called "Controller." Apply a the Drop Shadow effect here, copy it with property links, then paste it to your 10 layers. Now all the drop shadows can easily be controlled by one instance on your controller layer.
Thanks for the explantion.
To expand a bit on your question of how do you know whether or not a property has "links".
select the layer and double tap "u" on the keybord to rveal modified properties. Any properties with expresions will show up in red and you will see the expression to the right in the timeline area
Thanks for the explanation of the remaining issue.