Does anyone knows if there is a way to send an edit into media encoder and ask to export each clip of the edit separately (and even better, with handles)?
Yes, but not with Media Encoder. Assuming you're talking about Premiere and not After Effects, go to File > Project Manager. There you can select a sequence or sequences and export individual clips with custom handles. You can read more about this feature here:
The feature David describes works but I'm guess isn't what you're looking for. Project Manager will just export the raw clips - without any changes you might have made to them (e.g., color changes) within Premiere Pro.
Are you looking to be able to create daillies from within Premiere Pro?
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Render and Replace in Premiere Pro allows for this.
Select the clips in a Sequence, right-click and choose Render and Replace.
Set the Source to Individual Clips, then the Format and Preset, and enable Include Handles.