The real question is, the minimum fee we can pay is 1 sat, there is nothing less than 1 sat, right?
No one answered this question. The minimum fee that is less than 1 sat is zero.
Yes, zero fee is a valid transaction, but very few nodes will relay the transaction, and very few miners will include it in their blocks, so you almost never see them these days.
That is not precise.
If the transaction is valid, every node will broadcast it. The miners may not include it in a block, if there are transactions in the queue with a non-zero fee, especially while the mempool is over capacity for the next block. As soon as there is free space in the next block, zero fee transaction will get through - of course, the chance to empty the mempool below capacity is in question these days :-)