There are many CYP enzymes with varying roles in phase I detox and other activities such as synthesis and catabolism of steroids. They are divided into families and subfamilies with about a dozen members of families 1,2,and 3 being responsible for drug metabolism.
Here is a review of CYP enzymes and drug metabolism. It is fairly heavy going but you can just look at the figures and tables. Fig 1 shows the contributions of the differents CYP enzymes to drug metabolism and Table 1 lists CYP genetic variants known to affect drug metabolism.
You can compare your SNPs with this list.
I wonder, for example CYP1B1, do I have an increased or decreased activity of CYP1B1 when you have +/+ homozygous?
This entirely depends on the SNPs. They may have no effect at all - you need to look at the research for your particular SNPs and you need to understand that the presence of a variant often means nothing whatsoever.
The Self-decode entry you link is mainly talking about associations of SNPs and various conditions. Association doesn't mean causation and many of these SNP association studies are not very reliable. It depends how big the study was and how robust the statistics.
Here is the OMIM entry for CYP1B1. The only known disease caused by CYP1B1 variants is early onset glaucoma and the only robust disease association is with breast cancer.
ETA Variation in activity of an enzyme such as described by Self-decode isn't only attributable to SNPs in the gene for the enzyme. Changes in other genes or non-genetic factors can also be important.
