That noise is definitely related to a slipping drive belt. Double check the condition of the serpentine belt, if there are any excessively shiny spot, severe cracking, missing chunks of rubber, etc. - might be time to replace the belt. Note that fine cracks in the belt are OK/normal. If a pulley was wet, it could slip in that manner. Think it was just coincidence that it happened after the sparkplug repair. If the belt has more than 60K-90K miles on it - highly recommend thinking about replacing it.
It is weird that the car is running rougher - normally a car runs much better after a set of new plugs. Same make/model of plugs were used?
Also, nice clear close up pictures - thanks. Looking at the pic with all four plugs - assuming you mean cylinders #1-4, from left to right (cylinder #1 is closest to the pulleys/serpentine belt - passenger side of the car). My take on the condition of the plugs:
Overall - all four plugs show they have a decent amount of wear, probably could run them for a little longer, but the ash deposits are fairly excessive. They also show signs of running "rich" - though the factory tune of the car is fairly conservative and tends to err on running rich than lean. That grayish, powdery coating on the plug is the ash - these deposits form from the additives in gasoline and motor oil. A light coating of ash is normal, once they start to build up to that level, the likelyhood of a multi-cylinder mis-fire is greatly increased. From a quick visual inspection - #2 and #3 plugs have seen some mis-firing, possibly #1, more so on #3 plug. #1 and #4 plugs are better, with #4 being the best - perfect operation.
#1 - Heavy ash deposits, heavily worn center electrode (gap appears to be too open), dark, localized discoloration of porcelain and sooty deposit on the base ring indicate a possible issue with fuel injection in that cylinder. "Wet" base ring indicates a possible oil control/consumption issue with that cylinder.
#2 - Heavy ash deposits, heavily worn center electrode (not as bad as #1), dark, localized discoloration of porcelain and sooty deposit on the base ring indicate a possible issue with fuel injection in that cylinder. Again, "wet" base ring indicates a possible oil control/consumption issue with that cylinder. Due to the coloration - appears that this plug had issues with mis-firing.
#3 - Very heavy ash deposits, heavily worn center electrode (not as bad as #1), very dark, localized discoloration of porcelain and wet sooty deposit on the base ring indicate a possible issue with fuel injection in that cylinder. Again, "wet" base ring indicates a possible heavy oil control/consumption issue with that cylinder. Due to the coloration - appears that this plug had issues with mis-firing (worse that #2).
#4 - Light ash deposits, worn center electrode and ground strap (not as bad as #1, #2, #3), light localized discoloration of porcelain and medium, sooty deposit on the base ring indicates that cylinder and injector is running perfectly fine. Note that the base ring is much lighter in color, has less deposits that the other plugs - a well running engine will have all plugs look like this.
From this - I'd recommend that a mechanic run a compression test - make sure the engine is healthy. Possible that the piston rings are "stuck" or the valve seals are leaking an excessive amount of oil in to the cylinder. This is being transferred to the plug as ash deposits. If compression is good, then I would proceed to looking at ignition and fuel culprits. Possible that the intake side is clogged with heavy carbon deposits and/or the injector is not working optimally. Depending on the driving conditions - possible that the plug heat range is not matching up with usage of the car. Plugs appear to be too "cold" or the car is not driven enough. May just need a good blast down the expressway every once and a while, mix in some WOT (Wide Open Throttle) acceleration as well. Also monitor oil consumption, think about running a high-mileage motor oil (has additives that may help with stuck piston rings, break down internal deposits, maintain good viscosity, but can lead to more ash deposits - so monitor it closely). Do not be tempted to run a heavier oil - that just masks oil consumption and leads to larger problems down the road.