Do dark lines on porcelain dishes indicate usage of aluminium for the color? "I heard" that gray lines forming on porcelain indicate usage of aluminium in the coating. I would primarily like to verify this information.

Bowl #1 and bowl #2 have been used both for several months and were bought in different shops. The same observation goes for other dishes. Some don't feature lines, other dishes feature those after days already. The dishes who tend to display those patterns have been bought all at the same place (a large chain of stores specializing on furniture). The lines are most likely caused by cutlery as in cups the same lines are found forming ellipses at the bottom from the stirring. Again some cups don't feature those patterns others do.

Bowl #1 with no lines despite usage for a while:



Bowl #2 with lines:



Bowl #2 with lines - picture taken HDR mode:
If the two bowls look different although treated similar, the material must differ.

Your bowls are almost fully covered with a glaze - except for the ring on the bottom on which the ceramic was standing while fired in an oven. 

Here, water can enter the ceramic core. If the ceramic material of one bowl is more porous, water can be taken up easier. Upon heating, as in a dishwasher, the water absorbed expands. The glaze can't withstand the tension build up and breaks. 

This results in the cracks that you observe.