Does it work like the first games, pure gen 1 or is it gen 7, Pokemon having hidden abilities ?
Let's Go is a weird case. It's technically classified as Gen 7, complete with the modern type chart, Mega Evolutions and Alolan forms, but there are no held items, no abilities, only the original 151 (plus Meltan/Melmetal), and no breeding. See here for more information.
It is in the Kanto region, but it has features from gen VI and VII, which are alolan Pokemon and mega evolution. But I would say overall it is gen I.
It is generation 7. A generation is an era of the franchise determined by the release of a new region. For example, Johto started gen 2 with gold and silver. The reason why the let's go games are generation 7 is their release date being during the time of Generation 7. Heart Gold and Soul silver are Johto games but are generation 4 because they were released during generation 4.