Carbon steel pan problems, by symptom
Read your symptom, not the whole page.
"Food sticks, especially eggs"
Likely cause: the seasoning is thin, or the pan wasn't hot enough before the food went in, or too much oil is pooling. Try: wipe on a very thin layer of oil, heat until it just starts to smoke, wipe out the excess, then cook. Seasoning is oil baked onto the pan through polymerization, per Lodge's own explanation; it builds with use (Lodge). Not this: scrubbing hard. That removes what you are trying to build.
"Orange spots or rust"
Likely cause: moisture left on the pan. Lodge lists soaking, the dishwasher, air drying and humid storage as the ways cast iron rusts; carbon steel behaves the same (Lodge: How to Clean). Try: scour the rust off with steel wool, rinse, dry completely, oil lightly. For heavy rust, re-season in the oven (see the cast-iron care page). Prevent: dry on the burner for a minute after washing.
"Sticky, tacky surface"
Likely cause: oil applied too thick. Excess oil doesn't cure to a hard layer; it stays gummy. Try: heat the pan and wipe again, or rub it thin with a dry cloth. If it stays tacky, scrub with hot water and start a thin coat again.
"Blotchy brown and black colour"
Normal. Seasoning builds unevenly at first. Color is not a quality mark; a smooth feel and release are.
"Flaking black bits"
Lodge says seasoning can flake if layers haven't fully bonded, and suggests scrubbing with a nylon brush or salt, then rinsing, hand-drying and oiling (Lodge).
"The pan warps or hot-spots"
Carbon steel doesn't conduct heat efficiently, which can be an advantage for large vessels like woks and paella pans, where one portion of the pan is intentionally kept at a different temperature (Wikipedia: Cookware). It also means a thin pan on a strong burner can heat unevenly. Preheat gradually.
Which pan size?
Read the listing for cooking surface, not the outside diameter. For example, one popular French line lists an 11 in pan with an 8.3 in cooking surface. Another listing shows a 10.25 in pan with a 7.3 in cooking surface. If you cook for two, buy the size whose cooking surface fits two portions.