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The rattling noise can most commonly be caused by the timing belt tensioner.The tensioner can start to fail and creates a little slack which in turn on a cold start in most cases it will cause this noise but go away shortly after running.Even though your not due to have the belt replaced yet this tensioner can fail.I have also seen valve lifters/tappets start to fail and will cause this noise on a cold start as they can bleed down oil pressure and it takes a bit for them to pump back up with oil once the engine is started.
These will need to be checked into to then locate which is the cause and then repaired from there.
As for the coolant loss issue, it sounds like you have a leak since you have some wet areas.What has to be done is a coolant pressure test with a coolant pressure tester.Most shops or a dealer will have this tester and in some cases, a local parts store can do this testing as well.This will pressurize the cooling system to where once pressurized the leak will appear and then you will see for sure which component is leaking then that component can be replaced.I have seen loose or damaged coolant hoses or leaking water pumps as the main cause but also a head gasket leak as well.
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