Can a chemical be decomposed chemically

It will depend on the chemical, if it's a chemical compound, yes it can be decomposed chemically into simpler substances, further elements that constitute or make up the given compound.

Mixtures are separated by physical means as there are still separate entities as the substances required to make the mixture do not chemically combine or become altered chemically.

Elements cannot be decomposed into simpler substances as the simplest substance of matter is an element itself. This cannot be decomposed by chemical means.