When doing alignment, I would recommend using the same resolution for both RGB and depth if possible to aid alignment. In the RealSense Viewer, you may be able to further adjust the alignment using the Post Processing section of the settings. In these settings, there is a slider called the Decimation Filter that influences the resolution of the stream. By moving the slider backward and forward, you can see the image's resolution becoming smaller or larger.
On the RGB section of the controls, make sure that the Post Processing is enabled by clicking on the red icon to turn it to blue.
An easy way to tell how the Decimation filter is affecting the stream is to click the 'i' icon on the stream's toolbar to overlay its resolution and frame information. As you move the slider, you can see the resolution changing in the info overlay.
Regarding your question about depth, this link may be useful:
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Thank you for your interest in the RealSense camera.
The SDK offers a processing block for aligning the image to one another, producing a set of frames that share the same resolution and allow for easy mapping of pixels.
For more information, you can access the link below