.
It usually depends on how the speaker is thinking of the company-- as a single corporate entity or as a group of employees. I would guess the more usual is the singular, but this may be one of those BrE - AmE dichotomies.
.
Yes, you’re right about the context. The question or whether you make the verb singular of plural really depends on the relationship between the speaker/writer and the noun in question. In its simplest form:
My school/team/company ARE doing well
Your school/team/company IS doing badly.
It depends very much whether you consider the noun to be an entity (then it would be singular) or a group of people/individuals (then it would be plural).