Irritant Dermatitits. Yes; there are many chemicals that cause a form of eczema called contact dermatitis. You could be irritated by the chemicals or actually allergic to them.
Yes. Some chemicals can cause eczema rashes, including chemicals one is allergic to, chemicals that cause an irritating reaction in the skin, chemicals that are toxic to skin cells, and chemicals that wash off natural skin oils. People with sensitive skin should wear "non-latex" gloves when using chemicals, even household cleaners, bleach, alcohol, paints, etc., to avoid worsening their eczema.