Can I get posts with likes and other information from public profile of any user at Facebook, Twitter, Google+, Youtube and Instagram using their APIs, if I'm not logged in at any of these services? I need to use it developing PHP/JavaScript application. Thanks in advance.
Yes, you can. But there is one condition, the profile you're accessing must be public. Also one has his own API's so it can get a little tricky. I think you don't even need PHP because the APIs from google & facebook come in JS.
A tip that might help you. Try firebase. Firebase is a framework that makes client-side development easier. You can include Google APIs & facebook APIs.
I'm a native Spanish speaker so I'm sorry for my English. Anyway, check firebase. It should help.