Can my LN channel receive an LN payment greater than "X" for a certain amount "X"?
No, you can only receive payments until the entire channel capacity ("X") has been transferred to your side of the channel. At this point, you will no longer have any incoming capacity.
..or get several small payments that exceed "X"?
You may receive multiple payments that exceed "X", but you would also need to send payments between receipts (to move the channel balance back to the node of your channel counterparty).
What happens if:
(1) I receive 15,000 Satoshi orders / payments that are routed through the 100,000 LN node channel … or
Suppose your channel starts with 100% of the capacity on the node of your counterparty, then you could get 9 to 10 payments, and there would be no route to complete the last 5 to 6 payments.
I say 9-10 instead of 10, because each node participating in a channel must hold a small amount of capacity in reserve to close the channel in the event of a non-cooperative closure. So, if the capacity was exactly 100,000 sat and the payments exactly 10,000 sat, you will most likely not be able to receive all 100,000 sat payments sequentially as a result of this reserve requirement.
What happens if:
(2) I receive a 1,000,000 payment that will be forwarded to me through the 100,000-node channel (purchase of a "million-dollar" article).
As above, you may not be able to receive this payment due to the reserve requirements.
I think in order to run my shop, I would have to set up several giant channels to record potential payments … right? In both of the above cases, the channel must have enough data to accept the payments, and it can not receive payments larger than those contained in the channel.
Right, you can not receive a payment that is greater than your current incoming capacity on this channel (the remote_balance). As a shopkeeper, you can actively manage inbound capacity channels, but you can also allow customers to open channels directly with them. There are also services that allow you to buy incoming capacity etc.
