1. On an open channels, what happens if a node break? and is that the reason for a failed payments?
If some node breaks or goes offline then it can no longer route payments. Usually, such nodes are ignored during route construction as their peers should broadcast a channel update message stating that their channel cannot be temporarily used for routing.
Payments can also fail due to:
- no route to the destination,
- lack of liquidity in the route; in other words, you should be able to send less coins through the same route,
- out-of-date information about channels in the route,
- a node going offline while the payment is being routed.
The most common causes are the first two. Payments are usually split into smaller parts and sent through different paths to improve privacy and mitigate the liquidity problems.
2. How do i run a private lightening channel such as not to reveal or be seen by other networks?
All of the implementations you mentioned allow you to specify if you want your channel to be private while opening it. Private channels are not advertised across the network. They are not listed on Lightning explorers as well. I believe that most, if not all, mobile wallets create only such channels. Someone might learn that you had a Lightning channel through an on-chain analysis if either you or your peer closes the channel uncooperatively at some point. Channel openings and cooperative closes are indistinguishable from other transactions (involving multisig addresses).
Even if you have a public channel, no one beside your peer knows your current balance. Everyone can see the total capacity of your channel, though. It is possible to probe the balance through various techniques, but private channels are invulnerable as they are generally not used to route payments.
So, if you are really concerned about your privacy, you should open only private channels using mixed coins so that no one can reveal your identity if your channel gets closed uncooperatively. You can make your node run behind Tor easily.
