Is there any way of filtering by category in the control panel entries list?
Likewise, is there for an "entries" field (like how Playa lets you filter by channel, category)?
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You can via the search box:
myCategoriesField:"some category title"
See http://buildwithcraft.com/docs/searching for details on the syntax.
We do plan on making it possible to add category/tag filters to the element indexes though, including the modal selection windows.
Update: You can add a list of categories to the Entries page sidebar using the Category Sources plugin.