Hello,
1/
When there is snapshotting, it means that the core team propose a new "tangle file".
Is there any routine to check the conformity of the new tangle with the old one ?
I wonder if it would be possible someone propose a fake snapshotting.
In the future, each node will theoretically snapshot whenever they need to without relying on trust of a third party. Perma nodes will always be available for traversal of the entire history of the Tangle if necessary for certain on chain projects.
2/
With IOTA, there is no incentive to hold a full node ?
There is no direct financial incentive, you are correct. This is the same as Bitcoin. However the indirect incentive for running a node is to 1) not have to connect your light client to someone else's host and be at the mercy of their node remaining online, and 2) support the distributed nature of the network, without which the underlying currency that you hold is worthless.