I just finished reading part of the whitepaper of LN. and from the name "Network" it’s It's like a Twitter network.
It is nothing like Twitter at all. I suggest you try reading more of the whitepaper or wait until you have a better understanding of how it works before you try to create analogies.
I can open 1 channel to connect to the network
Or you can open multiple channels. The amount of access that you have to the network will depend on the channels that you open, and the channels that are opened by the nodes that you open channels to, and so on.
"just like when signing in into Twitter" and can be sent to all my friends connected to that network.
There is no "signing in" to the Lightning Network. It is a relay network, not a private entity.
That's almost what I understood that mean LN wallets will have full access to my private key?
Not if you are doing it correctly. You should never share your private keys with anybody. That is why they are called "private".
will be less protected than current Bitcoin wallets?.
Lightning Network is just a special way to use bitcoin transactions. Therefore, it is EXACTLY AS PROTECTED as those bitcoin transactions are.