touchpad problem it's lagging hanging and automatically moving

Well I will suggest you to updated your touchpad driver it any fix the issue because some time outdated driver can also cause this kind of issue. So I will suggest you to updated your driver if it is outdated.

I've also had mine shake the cursor around without my input and most of the time its dust or small particles that build up on it when not used frequently. I'd suggest cleaning it with some alcohol and paper towels, if the problem persists try running the Dell Touchpad Assistant app that should be preinstalled on your laptop (unless you used a debloater like AtlasOS) or Dell Support Assistant.
If after all of that the problem still persists and the laptop is under warranty then call Dell and have them fix it for you. If the warranty ran out then it might be worth it looking into a replacement touchpad and opening up the laptop to replace your current one.
P.S if you need a more comprehensive guide on how to open it I can provide one, I've opened it up a few times before and know most of it's ins and outs.