Are there genomics databases for neurological and psychiatric disorders? Are there databases that relate genetic disorders with neurological disorders? 

I am thinking of something like COSMICS for cancer? AFAIK cancer usually develops due to a combination of 5-10 mutations. 

Also if you can comment how genomics/bioinformatics in neurological contexts is compared to the how bioinformaticians study cancer? 

Related: https://www.nimhgenetics.org/resources/psychencode
Try with PsyGeNet:


  PsyGeNET (Psychiatric disorders Gene association NETwork) is a resource for the exploratory analysis of psychiatric diseases and their associated genes


It is based on literature mining and curated by experts.

Here is the publication if you want more details:

PsyGeNET: a knowledge platform on psychiatric disorders and their genes

and they even have a Bioconductor package for programatic queries:

psygenet2r: a R/Bioconductor package for the analysis of psychiatric disease genes