the size always exceeds 1MB
Not always, but it is usually the case. Some exceptions exist, for example:
https://mempool.space/block/0000000000000000000169070f8f0650ed43a83e1b22b99542c216c5933682ceOr does the 1MB ranges from 1 - 1.99MB ?
No, it is from few hundreds of bytes, up to 4 MB. Another example:
https://mempool.space/block/0000000000000000000515e202c8ae73c8155fc472422d7593af87aa74f2cf3dDoes the weight of a block (which doesn't exceeds 4MWU) determines the numbers of tx that could fit into it?
No. The legacy 1 MB part determines it. The number of possible created or consumed UTXOs remains unchanged, no matter if Segwit is enabled or not. And if Segwit would allow 1 GB witness, then still, UTXO creation and consumption would be still limited into this 1 MB legacy part.
However, if a single UTXO would handle more than a single user, then yes, you will have more "transactions", even if they would be represented on-chain as a single "transaction".
Is it possible to have an unmined block, even after the block weight has reached its limit of 4MWU maybe due to mining difficulty or other reasons?
Well, anyone can create a block template. So, even if you have no mining equipment, then by having just a CPU, and some full node, you can create a block template, and check, which transactions can go to which blocks.
And this is what sites like mempool.space do: they have their own mempool, with all waiting transactions, and then they guess, which block will contain which transaction, based on transaction fee, and transaction size.