This probably ought to be moved to security stackexchange, but not because it's specific to a particular security product, but instead it's specific to a specific security protocol.
However, I'll try to address the questions anyways.
Before I start, I need to explain how IKE and IPSec work together. It's not like TLS (where there is one set of logical keys that protect everything); instead (using the language of the RFCs), you have 3 Security Associations within this one tunnel:
- You have an IKE SA, that is used to protect negotiation traffic between Linux1 and Linux2 (such as negotiating traffic SAs).
- You have an IPSec SA that is used to protect data traffic from Linux1 to Linux2
- You have an IPSec SA that is used to protect data traffic from Linux2 to Linux1
Now, for your questions:
What is a CHILD SA?
A Child SA is any SA that was negotiated via the IKE SA. An IKE SA can be used to negotiate either SAs to protect the traffic (IPSec SAs), or it can be used to create another IKE SA. In the context you're seeing it, it's most likely a synonym for the IPSec SAs.
What is the difference between ikelifetime and ipseclifetime
No SA is eternal; they all have a best-by date; and when that expires, they go away (and hopefully replacement SAs are also negotiated, unless you're actually done with the tunnel). ikelifetime would be the lifetime of the IKE SA; ipseclifetime would be the lifetime of the IPSec SAs.