Does Shield Dust protect against attacks like Sleep Powder, Poison Powder, Thunder Wave, etc. things like that or certain attacks like that?
No, it only protects from secondary effects.
Shield Dust negates all possible side-effects whose probability would be boosted by Serene Grace: any side-effect would be prevented. It also blocks the side-effects of moves that have a 100% probability of a side-effect occurring regardless of Serene Grace, such as DynamicPunch. For example, Body Slam would only deal damage and not have its usual 30% chance of causing Paralysis. It does not stop moves that only cause these effects, like Thunder Wave. - Bulbapedia ` Source
>Shield DustThis Pokemon is not affected by the secondary effect of another Pokemon's attack. -Showdown
The secondary effect will not effect it, meaning the effect from an attacking move. Like sludge bomb will poison as a secondary effect. In short terms, NO