Do you believe that a company's brand color can influence client impressions?

Absolutely! There're numerous researches that prove this point. The color has an influence on our subconscious perception of things. Some "meanings" of colors are already embedded in our minds very deeply because of the culture we're surrounded with. Like, blue and green are calming colors because we see them everywhere in nature, and nature has a soothing effect on every one of us. And red color is now associated with something dangerous or passionate; it triggers our emotions. These are so basic levels of our psuchological structure that we barely pay attention to them.

Yes, Color plays a crucial role. Not only color but complete User experience will play the role. A product with rich features and poor UX will not fly high.

I don't believe it, it's proven. Color plays a part, but it's the overall brand that matters. Brand is much more than just colors. It's voice, tone, aesthetic, content, and perhaps most importantly, how the brand makes you *feel*.