Depends on the company. My company in the financial sector is always saying you need more financial acumen. I think it's mostly because out business people have no idea how to create a business process map or describe what they are doing.

It’s extremely important.

I’m currently in a position where I don’t have an in-depth understanding of the product and I can feel it when it comes to brainstorming.

As our product is a B2B where our users are sysadmins I have no contact with clients or use of the product. I think it makes it much more difficult to understand what is needed.

Where I see some of my client facing colleagues are on the forefront of understanding what needs to be improved.

It also depends on the person. I was a kid named Andrew who read Enders Game and the sequels growing up. I then went to an engineering university that emphasized “engineers have a duty to society and must understand the impact of their work” in multiple classes. So for me, the answer is “a fair amount”.

It really depends on the component under development but what I find is that devs that know the product can contribute to team discussions and planning far better than ones that don't.

Very context dependent.

If you're at a small startup, you'll want a lot.

When you're at a larger company, things typically get specialized, there will be dedicated product folks, and you'll find programmers with 0 product knowledge.

Product, Development, Sales are the three necessary cores to a product. That said, it's more a UX/UI role than development.