On my Mac I use Little Snitch to monitor outbound connections and I love it. I haven't found an equivalent simple and lightweight application for Windows yet.
Personally, I’d recommend using a combination of GlassWire for monitoring system changes and NetLimiter for the firewall.
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¹ — http://www.netlimiter.com/products/nl4
² — http://www.netlimiter.com/Files/ImageGalleries/netlimiter-4-...
[edit] Glasswire! https://www.glasswire.com/ It's super slick. Apparently the paid version has an "ask to connect" feature.
But I can see how this can be a disruptive process, when all you want is some work done. I wish we lived in a place where I did not have to use tools like this.
Isn't this what e.g. Zonealarm has been doing for 15 years on Windows?