I'm not understanding what you mean by running it 'standalone'. You mean running the executable directly? The problem is when you load the solution and begin debugging?
The WebClient object is going to need DNS/RPC accesss name privilege, and then the WebClient is going to need UDP access to DNS via port 53, subsequently it'll need TCP access via port 80. The former being D+ the latter firewall rules. Moreover, it may need additional D+ rules, i.e., either COM or Pseudo-COM access name access rights.
Since you're in debug mode there are several differnt components of the VS debugger that are instantiated. I believe if you set the global part of the VS debugger per my explanation in the bug report, a signifiant source of alerts should be mitigated. I think what's happening is a resource contention, i.e., IP access attempts simultaneously w/CIS alerts. Unfortunately the IP connection attempt is taking priority and until it times out the CIS alerts are stuck in the windows messaging buffer.
If the exe runs by itself, it sounds like the VSHOST for the project needs to have aforementioned privleges.