In the context of your description:
- sankhara means conditioned things / phenomena.
- dhamma means all things / phenomena i.e. both conditioned and unconditioned things / phenomena
What is unconditioned? Only Nibbana - it is that which is experienced by the mind, when it is completely free of all fetters and defilements.
What is conditioned? Everything else, including mental and physical phenomena / things.
"sabbe sankhara dukkha" means "all conditioned things/ phenomena are suffering / unsatisfactoriness". This does not include Nibbana.
"sabbe sankhara anicca" means "all conditioned things/ phenomena are impermanent". This does not include Nibbana.
"sabbe dhamma anatta" means "all things/ phenomena are not self". This includes Nibbana.
From AccessToInsight's Glossary of Pali and Buddhist Terms:
dhamma [Skt. dharma]:
(1) Event; a phenomenon in and of itself;
(2) mental quality; (3) doctrine, teaching; (4) nibbāna. Also,
principles of behavior that human beings ought to follow so as to fit
in with the right natural order of things; qualities of mind they
should develop so as to realize the inherent quality of the mind in
and of itself. By extension, "Dhamma" (usu. capitalized) is used also
to denote any doctrine that teaches such things. Thus the Dhamma of
the Buddha denotes both his teachings and the direct experience of
nibbāna, the quality at which those teachings are aimed.
Formation, compound, fashioning, fabrication — the
forces and factors that fashion things (physical or mental), the
process of fashioning, and the fashioned things that result. Saṅkhāra
can refer to anything formed or fashioned by conditions, or, more
specifically, (as one of the five khandhas) thought-formations within
Please see this answer for details.