.I have trouble understanding the following in bold.
1. Alicia is responsible for the country profit and loss account of her organization in Brazil. Her boss is the head of Latin America and he manages her closely against the P&L targets for Brazil.
In the above I'm confused about the meaning of "against". Is it saying "he manages her closely to make her achieve the P&L targets"?
"he manages her closely [against the P&L targets for Brazil]" - he makes sure that her work is measured against the targets, and that she is within the required parameters.
2. They need to be able to manage activities without traditional line management authority.
Does the "authority" in the above refer to "someone with power, your boss" or "official permission to do something"?
It is "line management authority" - the authority that is used in line management systems, where there is a strict hierarchy of managers and workers.
3. They need to be skilled at managing the complexity of a matrix environment: multiple bosses, conflicting priorities, and positive escalation.
I think I would interpret this as "intentional growth".