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.

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.