Great questions. Our understanding of chimpanzee's internal lives, or that of any animal, is limited. But, how they behave still gives us a window. For example, if a low ranking male chimpanzee waits until everyone else leaves before copulating (something I observed today), a reasonable explanation is that he has some understanding of other's minds. He knew that if other male's saw him with the estrus female, he may get beat up This is a pretty simple action, but actually takes a lot of cognitive process, grasping others' knowledge and intent.
Observing wild animals is one thing, but most of the breakthroughs in understanding the extent of thought in non-humans comes from cognitive experiments. Carefully controlling the settings of captive animals lets us rule out alternative and simpler explanations for their behavior. There are plenty of good examples on youtube if you search "chimpanzee theory of mind experiment." This can be done in the wild as well with things called playback studies.
I really recommend the book Baboon Metaphysics for fuller answers to your questions. Our biases will never leave us, but we can follow methods carefully that allow us to remove our biases from our findings.