Who determines bitcoin transaction fees? - page 2.

I've got two questions on bitcoin transaction fees, the first one relating to the bitcoin base layer and the second one relating to the second layer:

1) Bitcoin base layer - Who determines the bitcoin transaction fees? Is it the sender? For example, if the sender wants to increase the likelihood of miners including the senders transaction into the candidate block, then the sender can set a higher fee to compensate the miner? If this is the case, then how come most of the common exchanges have a fixed bitcoin withdrawal fee (usually around 0.0004 bitcoin or around $20), which I am unable to change?

2) Lightning network - If A wants to send to D and it appears that the only way to construct a route from A to D is if A goes through the payment channels A -> B -> C -> D, then does that mean in order for B and C to act as "intermediaries", they must be compensated by transaction fees? And if so, does that mean if we have A -> B -> C -> ... -> Z, then transaction fees would be really higher, potentially higher than if A sent directly to Z via Bitcoin base layer? And how are these transaction fees determined within the lightning network?

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