
"PUP" stands for "Potentially Unwanted Program". These are programs notable for dodgy behaviour and don't really benefit your system.
PUPs usually arrive by-way of installers. If you run an installer from the Internet, you need to slow down and read carefully what's happening; most installers will install additional spam software unless you decline these stuffty offers (and this is sometimes made difficult as they try to obscure the button required to disable it).
Intrusion Attempts are interesting. It's not always, but they're usually caused by Drive-by-downloads. What kinds of websites have you been to recently? It's entirely possible that some of this PUP software you've got is now attempting to communicate with an online server and is freaking Norton out, but it could be a separate thing entirely.
If you have Windows 10 (and probably earlier), you should open your Resource Monitor (open the Task Manager, go to the Performance tab, click Open Resource Manager) and then open the Network section at the bottom. It will show you a quick view of every program that is using your network. Wait until the next intrusion attempt happens, and at that moment see which programs are communicating. Check if your browsing is communicating more than it usually does, and also check for odd programs you don't recognise. It should give a clue as to what's going on.