does the sims 4 work for dell latitude 3340

@dominique30sept  You should be able to play on low settings, although the newer expansion packs (everything starting with Cats & Dogs) may be a bit more demanding than your laptop can handle, especially in combination.  Game and stuff packs are generally fine.  It will also help to not run anything else alongside the game, other than Origin of course, and you can put Origin in offline mode to reduce the resources it uses.

What you've described is not uncommon when people play on settings that a graphics card or chip can't handle; turning down the settings to low is the right response.  As for damaging your laptop by playing, that's unlikely as long as you make sure the laptop doesn't overheat.  Aside from excess heat, the only major source of damage to hardware is excessively high framerates, which you're not going to see with the graphics chip your laptop has.  Time and general use will also take a toll, but that can't really be avoided.

When people say that a game damaged their laptops, what's often the case is that trying to play revealed the effects of wear and tear already present.  Even a moderately demanding game like Sims 4 is going to be much more intensive to run than everyday apps like browsers, so if your hardware is starting to show its age, you'd notice it while playing before anywhere else.

Heat really could be an issue though.  If you want to be careful, install a tool like CPU-Z (free download) and open it before you play.  It doesn't take much in the way of resources and will show you the temperature of your processor in real time, so you can quit if it's too high, say above 90-95º C.