What happens if the commitment tx fee is too low? How often are commitment tx fees negotiated? 
Is it every time a payment is made and a new commitment transaction is formed? 
What about if there are no payments but both nodes see that the on chain tx fees are rising, do they renegotiate and update their previous commitment txs?
If Bob goes offline and never returns, but the latest commitment tx is very old and the tx fee is too small to be included in a block, is there anything Alice can do to force close the channel? (anything other than getting directly involved with mining). 
I believe "Child Pays for Parent" wouldn't work to help a force-close situation because the local output is encumbered by a to_self_delay relative to the time of it being mined, so the same miner couldn't include the "Child" in the same block. Is that correct?
Only if the state changes fees are negotiated (and for mutual closing the channel) so in case the onchain fees change and the channel is not used for a long time just send a fake payment hash to adapt to onchain fees.

Regarding 2 and 3. Nothing Alice can do. She just has to wait until the traffic on chain decreases. There are some ideas to include a dust level anyone can spend output to the commitment tx without timelock which could use cpfp