Always rinse your porcelain as soon as possible after a meal. Food particles left on the porcelain may discolor sensitive decor. Porcelain is particularly sensitive to food containing strong acids, such as apples or lemons.
Black lines on your plates are metal from stainless steel, especially from your cutlery. Always use rinsing or surface active agents if you use a dishwasher, as this makes the porcelain less susceptible to metal markings.
The greatest cause for scratches in the glaze, is when you stack the plates over each other in the kitchen cupboard. Use rinsing or surface active agents when using the dishwasher, it gives the porcelain a smoother surface and decreases the risk of scratches.
Carbonates in water can cause a gray coating which can dry to the porcelain surface and can be difficult to wash away. This can be removed by using ascorbic acid, citric acid or similar.
Påslsjö Fajans porcelain series Cercle Bleu is dishwasher safe. But if you want to keep them in good condition for as long as possible you should use a rinsing or surface-active agent. This reduces the friction, and you avoid unsightly scratches on your plates when you stack them on top of one another.