During the proof of work process, a miner receive a block to mine.

He mines it, whether the miner is rewarded or not, this block is added to his own chain.
So at once, his has a chain which is different from the main chain.
At this time could we say there are as many btc chains as there are miners ?

Next, is my understanding correct ?
The miner looses against miners, the block becomes orphan, and the miner's chain reverts back to the main chain (somehow) and he waits for the next block to be mined.

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Hi,

How to see transactions that occured in the off-chain part ?

I understand LN will register finally the balances on the blockchain, but what about all the small transactions during the off-chain process ?

Will there be a blockchain.info like tool to explore all transactions ?

Blockchain should be transparent and be able to register all transactions. If LN allows off-chain small transactions for performance purpose, fine, but how to ensure transparency ?

I might not understand well the final process of registration of the balance sheet on the blockchchain, will it show all transactions between Alice and Bob ?

So many questions  Thanks all.