Will placing inductors near each other have adverse effects?
While the inductors you have selected appear to have ferrite cores, the ferrite does not provide a complete magnetic path for the coils. Therefore, there will be a significant external field, with the possibility of "adverse coupling" among multiple coils.

If this is going to be a problem in your application, consider shopping for "shielded" inductors, which do have a complete magenetic path in ferrite, minimizing the external field.

Another way to minimize coupling is to orient the inductors' axes at right angles to each other wherever possible.