water out the cold exhaust or after standing for awhile is normal built up condensation, should clear after a long cruise. black dripping water is just water vapour picking up old soot from pipes. I'd only worry if it continues to steam/smoke after a long good hot blast on a warm day.
first diagnose if it's a failed HG.
- check temp sensors terminal pins r clean.
- remove temp gauge sensor & ecu coolant sensor & test they're within spec resistances.
- make sure after changing coolant system that it's been fully bled, heater dial set fully hot, rad brimmed with cap removed, start engine & hold 2k till it goes 82c and thermostat opens and bubbles purge, keeping it brimmed at all times, keep going till fan runs on/off 3 times, blip occasionally to further nudge the bubbles out the system.
- with the system fully bled n hot, blip the engine few times n spot if it bubbles soon after each blip constantly, which could mean a blown fire-ring.
- a more accurate test would be to get garage to test the bubbles in coolant for monoxide to verify it's a HG failure.
if HG failed it could be:
surfaces wasn't precisely flat or checked,
wasn't clean or dry,
head bolts & threads not fully cleaned,
wasn't torqued to factory spec in factory procedure
have a word with the shop.