Even when inflation is close to zero, interest on debt means that a company that isn't growing won't be able to service it's creditors forever, and it'll fail.
There are plenty of reasons why 'growth at all costs' is a stupid goal, but there does have to be some growth for a business to survive.
Growth is desirable for investors, but it's not at all necessary for a company to continue operating.
That depends on what exactly is growing. As long as profits are growing by more than 0%, then the company is growing, regardless of inflation. If its only revenues that are growing in the low single-digits, then still the company could be growing! Inflation is the phenomenon of prices generally increasing, but no matter what anybody tells you it is not distributed equally. Just because the overall rate of inflation is 5% does not mean that your costs have increased by 5% YoY.