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Because you say mechanical that ~~does~~ might preclude chemical reactions...
At least a basic level of a real world self-replicating "device" in an abstract sense, you can "grow" some crystals given sufficient substrate liquid.
I think it is theoretically possible, and may be easier to realize at a microscopic scale since you can get a sufficient amount of liquid that can be considered a 'functionally-infinite' space and the device can more freely float around without having to worry about needing complex dextrous parts to put things in the right place.
A loose ball of dandelion seeds I put together would be my idea of a simple self-replicating 'device' that operates mechanically, in the natural world, at a human scale that I think meets your criteria. It floats around in the area and if there are dandelion fields where it goes, it can pick up the seeds, and if it bumps into a random obstacle in the landscape it will break into parts that can pick up other seeds. The only logical aspect of the device is how many seeds it is comprised of, and there is not a set sequence as to when it will break, because it just depends on where the wind pushes the 'device' into in the landscape.
Addendum: Condition 4 is hard to get around with my example, I can't guarantee that when it breaks apart only dandelions that weren't part of the original part would formulate the new part. Seems overly perscriptive if you count using its own constituent part to make a new part, then repairing itself up again as contravening that condition.
Precluding chemical reactions would pretty much make this impossible, given that any non-trivial machine would have to refine raw materials which would involve chemistry.
Permitting chemical reactions makes this trivially provable because evidence of self-reproducing chemical machinery is all around us.
You're absolutely correct on that. For the sake of the thought experiment and trying to keep to the spirit of the conditions, my dandelion ball device is internally, a purely mechanical device. The chemical and biological reactions related to growing dandelions and natural wind, all of that I consider external to the device.