I had a go at making the basin, I’m not an expert so dont now if it the right way but, it seems to work.
I started with a sphere (16 segments 8 rings) Delete the top vertex (pole). Make the top into quads by joining edges and loop cutting to fit. Then select all, Alt+Shift+S (scale to sphere to make the top rounded). Next delete the bottom half of the sphere and rotate all 90 degrees, now delete the top half of what’s left then add a mirror modifier and move the mesh outwards to establish the length of the basin hole. Apply the modifier and then bridge the edges of each half. Then add some lop cuts across the join to make the resulting quads as square as possible. You should now have half a pill shape. Select the upper edge loop and hit E, then rightclick, then alt+S, and scale this extruded loop outwards just slightly(this will effectively give you an outer edge loop for the rim of the basin hole.
Select the new edge loop and hit Shift+S (cursor to selected), whilst still in edit mode add a plane and scale it to be slightly bigger but the same proportions as the ‘pill’. In face select, select this new face, and hit X>faces only. Now subdivide this empty plane (ctrl_E) to get enough vertices to roughly match the hole’s. Next start making quads by joining the pill to the new mesh. I found it better to join the end pieces first (because they matched well after subdividing) then get the rest to match by subdividing edges and moving the resulting vertices around a bit, just remember to make quads. Now add a lower edge loop for the rim of the basin. So now you should have 3 loops making up the basin edge (no creases, this is why there was the extrusion earlier). Then you just need to extrude the back edge to for the overall shape of the basin. Add some edge loops along the outer edges to make the corners more angular.
For the holes I selected 4 faces then extruded and scaled them in to size. Then extrude into the model to form the hole. Now hit X and delete faces. You should have 2 square shaped loops made up of 8 verts each. Select 1 loop and hit Alt+Shift S (scale to sphere), do the same with the other loop. Go into face select, and selct the whole inner faceloop by alt-Right clicking on an edge the runs 90 degrees to the direction of the loop, Extrude and alt+s just slightly to form an outer edge loop for the hole (same reason as earlier, just done in a different order). Add an inner edge loop to the hole.
Here is a Blend…http://www.pasteall.org/blend/24713
When I extruded the first outer edge loop, I for some reason used just S (not alt+S) that’s why the verts dont line up along those to loops. But when you do it it should be fine. Hope that explanation makes sense, and remember it could be all wrong