In most of the results that you've provided, the spikes in latency start right at hop #2 - which would imply that the issue is originating somewhere between hop #1 (likely your router/modem), and hop #2 (the first step out to your ISP). This information, paired with your description (the spikes occurring whenever you do anything online) would imply that the cause of the saturation is from your own network.
Bandwidth saturation happens when you use more bandwidth than is available on your network. With a 1Mbps connection, it may be a bit more easy to run into a situation like this. We've got a section of our manual that goes over this topic in a bit more detail:
http://www.pingplotter.com/manual/scenariosaturatedpipe.htmlIf you have any other questions - please let us know!
Best wishes,
-Gary
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