Can eczema be transmitted by scratching someone really hard?

Answer 1

No.

http://www.webmd.com/skin-problems-and-treatments/guide/atopic-dermatitis-eczema

http://www.mayoclinic.com/health/eczema/DS00986/DSECTION=causes

http://www.nhs.uk/Conditions/Eczema-(atopic)/Pages/Causes.aspx