Is there any free database when one can check the gene frequency in a healthy population? For example I would like to check it for genes like BIN1, CLU or CR1. On the English Wikipedia I found a gene frequency for APOE gene (for example: 79% for e4 and 7% for e2), and it was linked to the specific publication. I wonder if one need to look for specific publication when looking for information like that or there is any database with such information available?
You can find some, but not all, gene frequencies in a range of populations at The Allele Frequency Net Database - Allele, haplotype and genotype frequencies in Worldwide Populations.
However, your question is broad genes have a lot of variation within them, the most basic being Single Nucleotide Polymorphisms (SNPs) and you've already been pointed to one source of information (SNPedia which is new to me) but you can look at the variation of allele frequency of SNPs in different populations by looking at dbSNP1. Note they have a subset for variation associated with clinical phenotypes.
1 This may be the source on which at least some of SNPedia is based as dbSNP has been around for a very long time.