I've bn recmnded Advantan scalp solution by my dermatologist to treat my scalp eczema. I'm now on the 2nd course of the soltn as the eczema is still present. Will this steriod soltn cause my skin and hair to thin whilst treating the eczema?

Don’t use too often. What was the frequency of application recommended?
You can use the scalp steroid solution every night for a week or 2, then as the condition improves use it every other night or twice a week & then as needed.
Skin atrophy is a risk from overuse of the steroid. Too frequent application of high potency steroids.