I would argue that it is even somewhat safer to use a neighbors WiFi than your own internet, although this is only for two specific reasons. The feds can trace live WiFi but if they don't trace a connection while it is live there is a good chance that they will never be able to determine that you were using the open WiFi for the session they are interested in, if you spoof your MAC address then it is even less likely.
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It is worth noting that if you are rooted even if you are using WiFi there is a good chance you will be fucked, I am not sure the accuracy of WiFi Positioning Systems these days but I imagine if the feds can gain remote control of your WiFi card that they can remotely geoposition you accurately enough to determine who you are, though in apartments that share walls they might not be able to differentiate between you and your neighbors.
I'm not sure what you mean by this; are you coming from the perspective of an active hunt for a person when they're actually in the area? If so then I can see what you're saying, but if you just mean when they aren't even within range of the WiFi signal to begin with, I have no clue how it could be harder for them to identify you after the fact -- none whatsoever. Have a reference handy or something?
I'm not saying you're full of it, mind you, I just have no clue how it could make a difference and would like to.
I don't know what you are asking really. If I use a neighbors open wireless router and then I move, and two weeks later the police show up at my neighbors house, there is very little chance that they will be able to determine I am the one who was using my neighbors WiFi. So it adds potential unlinkability in some cases, although for the best additional security you would need to be moving around using random WiFi access points. If you are in a static location using open wireless networks you are not giving yourself a huge benefit, if the police show up before you get out of the habit of using a particular network they will be able to do a live wireless trace back to you. It is even possible for the police to determine who is using wireless networks without doing a live trace if they can determine multiple locations that were used by the same target (This is how they got that general Petraus his mistress, she used WiFi from hotels over time and although the FBI never got her with a live WiFi trace they did an intersection attack on the names registered at the Hotels during the multiple sessions, and her name was the one that was uniquely in all of the crowds). So WiFi is not a magic bullet, but it can definitely add to your unlinkability and untraceability, even if you are using WiFi from a static location such as a neighbors house. Using it from a static location is not going to greatly increase your anonymity, but I like to know that when I move to new locations my previous sessions are much less likely to be linked to me, whereas if I use my own internet and move to a new location it is still possible that the police could end up tracing back to me via a prior session. That is the benefit of WiFi, even if all of the Tor nodes on my circuit keep logs and the police take half a year to get court orders to follow them back to me, if I used WiFi of a neighbor and moved to a new location in the mean time, by the time they get back all the way to my neighbor there is not a log for them to follow to me anymore, and I am no longer in the habit of using that WiFi location so there cannot be a live trace. It doesn't mean they can not use other methods to deduce it was me, and if they do multiple trace backs to multiple locations that were near me they could do an intersection attack and various other things, but I would argue that it is still definitely better than them tracing back all the way to an IP address that was registered to an account under my name. At the very least it provides some plausible deniability for court, a jury will be less happy with "We followed this signal back to here and then it went dead, but we are pretty sure this person a few houses away was the originator of the signal".
Maybe if you clarify your question I can answer it better I really am not sure what you are asking. If it is in regards to WiFi Positioning Systems what I mean is that if somebody roots your computer and can see the wireless access points around you and their signal strengths, they can geoposition you with this information, and it could let them tell which house or apartment the signal is originating from.