I would try a powered compactor (I rented one at Home Depot). This is not the perfect stone to use but I think it will be fine (though this is something i usually leave to professionals. )

Gravel is fine. Rent a powered compactor as stated and then put down a layer of stone dust after compacting to provide a manageable base to fine tune heights for the pavers.

Stone dust is a bit coarser than sand and won't find its way through the gravel like sand can.

check this link:

https://www.icpi.org/paving-systems/concrete-pavers/installation

The danger is not that the stone can't support the patio. It can. But over time, a sand setting bed could migrate down into the stones, causing uneven settling of the pavers.

Is the first picture an area you will be paving? It doesn't look like you can build on top of this without getting to high on the foundation, or without raising the fence.

I think if you added an inch and a half or so of paver base on top of the gravel, and mix it in a little before compacting, it would be sufficient to slow or stop the sand migration into the gravel. And then add the sand setting bed. But again ... grade elevation ... need to get that worked out. You don't want to create a nice patio that destroys house wood or invites termites.