In a Lightning Network who commits to the blockchain the final transaction?
So let's imagine a Lightning Network made up of thousand of nodes. Transactions are routed until the moment comes where all the channels need to be closed and commited I presume. Which node actually takes care of this?


No, that is not how lightning works. All channels are not created and closed at the same time. They are created individually and closed individually. Each channel has its own 2-of-2 multisig, not the entire route. And channels are not established just for one route, that would be inefficient. Routing happens because there are channels that are already open between people and it is more efficient to route than it is to establish a new channel.

When a channel is closed, the two people in that channel will create the final commitment transaction for that channel and once that is broadcast and confirmed, the channel is closed.


  who will actually pay the fees to the BTC network?


With the current lightning protocol, the person who requested the creation of a channel will be the one who pays any transaction fees. Although if both parties mutually requested the creation of the channel, they can probably split the fees with a bit of manual transaction modification/creation.


  Whoever is listening and has the transactions in hand can build this huge transaction (as long as the timelocks are respected) and soon it will be mined.


No. Commitment transactions require the signatures of the parties involved in the channel.