Water/coolant will not show up on the dip stick other than an increase in oil level (water settles to the bottom).
Soot on the plugs looks more like fuel than oil to me but its hard to tell. Any chance that the carburetor was flooding causing very rich mixture resulting in the poor running and soot?
Coolant level is a difficult measure of coolant loss into places it doesn't belong. A coolant system pressure tester will help identify if there is a leak and where it may be.
