Might be more than one problem, but the thumping when you're stopped does not indicate a suspension issue typically. Try it idling in reverse, in drive, in park, ... bring the RPM up to 1000 and see if it stops or changes, sounds more like exhaust vibrating against something or sagging engine/trans mounts, needs further investigation.

The hard ride is likely accumulators, or your ride-height is too high.

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