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Are all these representations supercuspidal

First of all, you will only get a non-trivial inner form at finitely many places (where $D$ ramifies). Even then, the group is not compact mod center, so not all representations will be supercuspidal …
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A trace formula for $\mathrm{GSp(4)}$

There are many kinds of trace formulas on a given group $G$, and different things you could mean by decomposition of the spectrum. As mentioned in the comments, there's Arthur's article in the Shalik …
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