Are Lightning invoices->addresses permanent?
No, Lightning Network invoices are not reusable. Every payment invoice contains a hashed payment secret which is used to construct an
HTLC.
Can I generate somewhere address without amount? (Just clear lightning wallet address and I don't mean refill address BECH32)
The Lightning Network does not use addresses like the first layer. Implementations like c-lightning and LND support sending/receiving keysend (spontaneous) payments. Such payments do not require payment invoices; you just need the id of someone's node. Most wallets support only payment invoices.
For example if in Blue wallet I will generate invoice for 1$ (you must fill some amount of invoice) and it will give me address...
Keep in mind that refill addresses are unique to BlueWallet. Their Lightning wallets are custodial. You don't have to worry about opening channels and inbound/outbound capacity.
Can I receive satoshis forever and in any amount?
No. Even though you are using a custodial wallet, BlueWallet has a limited number of channels with limited inbound capacity. Once they run out of inbound capacity, you won't be able to receive any satoshis. Any payment might also fail if: there is no route between BlueWallet's node and the sender or if intermediary nodes do not have enough liquidity to forward the payment. Large payments are usually automatically split into smaller chunks which are routed through different channels. It increases their success rate.
How would you for example withdraw Lightning Bitcoin from some payment gateway?
You would very likely have to manually generate an invoice with an amount specified by them. That's how withdrawals work on Nicehash, Bitfinex and other Lightning compatible services. You could also use
BTCPay Server which would use your own Lightning node. However, you would have to learn how to manage your node's liquidity (incoming/outgoing capacity) which is difficult.
How will they open channel or connect with me?
Unless you open a direct channel to them, your withdrawal will have to be routed through your other active channels.
Sorry for (maybe) dumb questions but I am not Lightning network pro
Feel free to ask any questions! You may also find
The Lightning Network FAQ and
Basics of The Lightning Network useful.
