PCB design avoiding errors
It looks fine in terms of spacing between components. 

The labels you mention, I assume that this is the silk screen for components ID etc? If so, then that can be anywhere, it will not affect the circuit, so that is fine. 

Of course if you use DIP8 IC's you can put an IC socket in there before mounting the IC, that is not a problem.

The best way to check for errors is to do a DRC (Design Rule Check) which should highlight any errors in the layout. I have not used EasyEDA before so I do not know where it is but in most design software packages it is pretty easy to find