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)?
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.