Question about the quantity of orchid species and genera
The Plant List records 27,801 accepted species names in 899 genera within Orchidaceae. This estimate probably differs a bit between authorities. For example the Angiosperm Phylogeny website records 26,000 species in around 880 genera. Regardless it is I think the most speciose angiosperm family. 

The explosive diversification of orchids, like the diversification of angiosperms, has been a big study point for evolutionary biologists. A lot of explanations center around the wide array of floral morphologies which you can find in the group, as well as (although not independently) the evolution of a whole range of pollination strategies. Other factors include evolving in a tropical environment and the evolution of CAM photosynthesis in the group. You can find more details in, for example Givnish et al. 2015