Yes, there are multiple ways of creating this. I think the best is always to keep the author experience in the component vs sending them to a different page/section of AEM. You could have different configuration per type of breakpoint either with TABS (if the 'n' is fixed), or with multi-fields (if 'n' is variables). Also, you should look into separating the 'data' from the 'asset', in the sense that the image should be the same, or associated to the same asset.
For example, in the case of the carousel: You could have a tab with a multifield for each slide, with three sets of fields one for the image reference, one for the desktop data, and one for the mobile data. For each new slide, you allow the user to 'add' a new set of fields that repeats to 'n'. You can even allow the author to change the order with up/down arrows.
In this setup, you should create a rendition specifically for the mobile breakpoint (create renditions either with with a workflow manually triggered or when asset is uploaded, up to you) and have the carousel serve the image rendition that corresponds to the breakpoint that the user is in (ie mobile, tab, desktop). With this, by default the image would be the same, but the author can overwrite the rendition in the DAM if the image needs to be different, and the links/text would be specific to each breakpoint.
