Is 2KMovies safe?
Yes. The site asks for nothing: no account, no email, no card, no app store, no file to run. It stores three small things in your own browser, which are your list, your viewing country and the episodes you mark, and it sends none of them anywhere. Posters come from the film database that supplies them, and the only outside links are the Watch now buttons, which open the title on a named service. Nothing on the site can install itself on your device.
The question comes from the copies, which paid their bills with pop-ups, fake download buttons and players that asked you to install something. The address page explains how to tell this site from a copy; the short version is that this site never asks you to install or pay for anything on the way to a title.
Is 2KMovies legal?
Yes, in every country the site covers. Reading about a film, following a season and keeping a list is ordinary browsing. The viewing happens on the service you pick from the Watch now list, and that list is made of licensed services operating in the country you chose: the subscriptions, the free ad-supported tiers and the rental stores. Change the country and the list changes, because licences are sold country by country; that is the whole mechanism, and it is what keeps viewing legal wherever you happen to be.
How does the site pay its way?
The plain way: when Watch now takes you to a service and you take a subscription or rent a title there, some services pay a referral fee. The price you pay is the service's normal price; the fee comes from the service. There is no premium tier and no paid membership.
Children and family viewing
Every title page shows the genre chips and the synopsis before anything plays, and the animation and family collection gathers the titles made for younger viewers. The age rating and the parental controls belong to the service you open, which enforces them on its own player.