The Live Perspective Filter from the Filters Studio lets you create perspective distortions. Regarding the tools (perspective and mesh warp) i believe they will be added at some point. They are not the only features missing - currently you can't create macros on the iPad version for example.
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1 - Drag the adjustment layer over the layer you want to affect or over the thumbnail of the layer you want to affect in the Layers panel to clip it or to "mask it" (nest it) to that layer respectively. Both will work. See this video tutorial for more info: Clipping vs Masking (Affinity Photo)
2 - Make sure you have one of the selection tools active to move just the selection, not the Move Tool.
3 - These tools are not available in Affinity Photo for iPad. Affinity Photo (desktop version) does have them.