Pathclear or Bayer Path Weed control - the ones you mix up in watering can and water on are the best. As for the lawn/slabs question, take a half moon edger and use it to take out half an inch of the lawn, to depth of at least an inch, where it meets the slabs, then use edging shears to keep the edge clipped back whenever you cut the grass.

My lawn meets some of the patio and after I have mown it I use the strimmer to cut along the edge then run the mower over again to suck up the bits.

I have just discovered the wire brush clipped on a handle suitable to my height......other tools used on same pole.....is really good for rubbing off seedlings in paving crevices before they get too large and visible. Done for a short time at intervals it is quite therapeutic, too long a session makes my hands painful. First time for ages my frontage blocks are clear of weeds.