Adding button inside grid, checkbox inside grid.

On each row of a grid and advanced grid you can't add buttons with custom actions, you can add a general button on the bottom (or top) in order to open the pop up with the current selected row. For multiple delete function, you can also enable multiselect and add a button again to do the deletion, or you can use Advance Grid from the marketplace (https://marketplace.ptc.com/apps/229413/grid-advanced---version-411#!overview) which has editing capabilities and for deletion it's exactly what you are describing.

If you want to have to capacity of adding buttons and different widgets on the rows, you should use the Repeater Widget instead (on where each row it's a mashup).