In the invention of lying we see a culture where nobody lies. They don't understand what it is to say something that 'isn't'. The way everything is staged in the movie feels foreign and odd. Thinking about little social behaviours, taking them out, and envisioning what culture and language would be like without them gives a view to this, and shows the impact that language and culture have on thought and behaviour.
Think of the way language shifts, and how it effects people's thought process? As well, social evolution, if I am remembering correctly, has had huge impacts just based on the development of language. It adds form to thought, focuses it, allows one to express and compare ideas.
Seems like a foregone conclusion.
Imagine in your language you did not have a word for time, thus time isn't a concept of which you can understand without learning a new word in a new language. Language categorizes and organizes our sense data. As of culture I am less sure, you could suggest that certain types of slang arise in certain cultures, and thus effect how we understand. Or even more simply one culture may have different values to another culture and thus you may value courage in one culture and humility in another.
Yes, I think that the way that I think is shaped by language and culture, because we are all a product of our experiences. If a person has experienced life differently than I have, they are likely to have different opinions about things. You might have different traumas or different success that affect your beliefs.
Language, we could argue, constructs human experience, and culture, too, can organize how we experience ourselves in the world. For instance, Western "Enlightenment" ideals posit a progressive destiny for humanity, and Christian traditions paint mankind as the center of it all, not as a speck of dust in a vast cosmos. I have been shaped by these; even the very idea that there is a "meaning" to life itself is something I can't quite get rid of, even if I try to think in an egoless, cosmic way.
Someone's culture clearly shapes how people think. "It takes a village to raise a child." Someone in sub-Saharan Africa thinks differently from an Afghani tribesperson who thinks differently from an American growing up on Cape Cod. Those three people were raised in different backgrounds and probably have vastly different worldviews and different concepts regarding religion, materialism, consumer activity and lifestyle.
A language is just a way to express yourself, and culture is just where you come from. The two have nothing to do with the way that you think unless you are racist or something. It should have no influence on your thoughts, as they are just forms of expression.