Your blockchain must have all of the following properties:
- It's a merkle tree, or a construct with equivalent properties.
- There is no single point of trust or authority; nodes are operated by different parties.
- Multiple 'forks' of the blockchain may exist - that is, nodes may disagree on what the full sequence of blocks looks like.
- In the case of such a fork, there must exist a deterministic consensus algorithm of some sort to decide what the "real" blockchain looks like (ie. which fork is "correct").
- The consensus algorithm must be executable with only the information contained in the blockchain (or its forks), and no external input (eg. no decisionmaking from a centralized 'trust node').
If your blockchain is missing any of the above properties, it is not a blockchain, it is just a ledger.
1- Merkle tree is not necessary. This is only used for efficiency. Mailing around CDs and verifying with SHA sums would be sufficient to implement blockchain.
2- There is contention on whether the next point applies.
3- Strictly speaking, considering the speed of light, no two nodes can agree on the full sequence of anything. Setting that aside, there are some blockchain topologies where forks don't happen
4- Yes!
5- This is true in theory. But actually it fails when computers are controlled by humans.