Eliminating Slivers or Combine shared boundaries

Hi

I have two polygon layers (1. Conservation polygons and 2. Forest polygons). Unfortunately these layers came from two different sources, so as a result any boundary between these layers have gaps and overlaps.

I want to clip the conservation layer to the forest layer to identify what areas of conservation are found within forest polygons. This layer that has been identified within my forest polygons, I now want to erase from my original forest polygons, but unfortunately as the boundaries to not match, anywhere there was a gap or overlap, slivers are created.

1. Is there any way to ‘snap’ these boundaries to show them as one boundary or
2. Using one layer as main layer, move the boundary of secondary to match main layer or
3. Eliminate areas using the boundary of a different layer

Hope this not too confusing.

Thanks