1-How to identify the wild-type of an SNP? for instance the SNP D19H rs11887534 of ABCG8 gene, you have the DD, DH, and HH. I know here that DD is the wild type. But is there a database where all of this is clear for different genes?

The term 'wild-type' is not well defined when considered in the context of a population study looking at multiple diseases. A particular SNP may prove beneficial to some diseases / conditions, but detrimental in others. Keep in mind that most diseases are dictated by complex genetics. I elaborate on some terms here: A: Definition of minor and major allele and connection with risk, effect, wildtype

You may want to look at the ClinVar database and the NHGRI GWAS Catalog.

2- Is there a database that clarifies the effect of SNPs on the function of a gene (in vitro studies), or animal studies?

You may want to look through some of these: A: How to choose good tools for identifying functional SNPs?

Kevin

I would not make my life too difficult and simply take the nucleotide that is in the reference genome as wildtype. It is true that population-specific genotypes might not be well-represented with the current reference genomes but unless you are specifically interested in a certain ethnicity better stick with your reference genome. Simply look up the rs number at dbSNP.