Can I break up stones and overlay soil to grow lawn?
I don't think that expanding foam stuff will split granite.  (Looks like granite in your pix)

To directly answer your question:  If you can break up the rocks, then go for it.  I think you need 6" to lay decent grass.  Normally grass will send roots several feet deep.  The areas where there is thin soil over rock will turn brown earlier in the summer, tend to grow more slowly, be more sensitive to over/under fertilization.

So:  If you can, remove the rocks completely.

Your pic looks like some of them are flat rocks that were laid in place.  If so, buy a rock bar (think 6 foot long straight prybar) and sink it into the ground beside one, put another rock as a fulcrum and pry.

The narrow one sticking out further back I suspect is the upper edge of a chunk of bedrock.  While you might be able to remove it, I suspect it's more work than it's worth.  How about putting a ring of earth around it for a flower bed.