Facebook – Do Friends Get Notifications When Liking a Photo?

Contests/competitions/sweepstakes/etc

must not use Facebook features or functionality as a promotion’s registration or entry mechanism. For example, the act of liking a Page or checking in to a Place cannot automatically register or enter a promotion participant

and

must not condition registration or entry upon the user taking any action using any Facebook features or functionality other than liking a Page, checking in to a Place, or connecting to your app. For example, you must not condition registration or entry upon the user liking a Wall post, or commenting or uploading a photo on a Wall

and

must not use Facebook features or functionality, such as the Like button, as a voting mechanism for a promotion

See Facebook's Promotion Guidlines for the rest of rules and regulations.

Facebook Pages are public, subject to any country and age restrictions set by the Page administrators. There's no way to hide your activity on public Pages administered by others, from casual viewing or from Graph Search. https://www.facebook.com/help/329858980428740

For Facebook Groups, it depends on how the Group was created: https://www.facebook.com/about/groups

Secret: Only members see the group, who's in it, and what members post.

Closed: Anyone can see the group and who's in it. Only members see posts.

Open (public): Anyone can see the group, who's in it, and what members post.

Finally, no users can tell if someone has visited their timeline, either through the web interface or through an app. https://www.facebook.com/help/205685226136386