What happens to extinct blockchains, and transactions inside of them?
This process, generally know as forking, creates two parallel chains that are incompatible, that is, there will be some transactions that will be valid against one chain but are not valid against the other.


If there are parallel branches, a miner might keep track of both of them. Once a chain is rejected, transactions in that chain are checked against the accepted one. Incompatible or duplicate transactions are simply discarded, while the remaining can be held over to go in the next block (or blocks as there might be too many transactions for just one).
Transaction records will remain in-tact for the accepted chain, but records for the rejected chain will be merged in to the old branch as described above. It would be impossible to attach these transactions to the final block before the branch, so, they are kept around by miners and put into the block chain as normal.
There might be a bit of confusion here... once a block is mined, it can't be changed, so it's impossible to store further transactions in that block. Furthermore, this block will have exactly one coin-base transaction. Any transactions that happen after it is mined will each be stored in subsequent blocks that follow it, but each of these blocks will have exactly one coin-base transaction, as is specified by the bitcoin protocol. So yes, there will only be one coinbase transaction in the block generated by A.