1. Do I need to call the parent constructor in B's constructor to initialize the value owner in A
Unless you are passing arguments to a constructor, you do not need to explicitly call it. Assigning owner = msg.sender will be evaluated when the contract is deployed
2. Does B need its own address, or will it just use A's as its own?
Using Inheritance in Solidity will bundle your code together and deploy it under a single contract
From the solidity docs:
When a contract inherits from multiple contracts, only a single contract is created on the blockchain, and the code from all the base contracts is copied into the created contract.
