What are the exact speed limits for charging and hacking/deploying/xmp firing?

The existence of speed limits has been known for a while (I asked about those more than a year ago) but, as usual, Niantic never disclosed the exact values. Experimenting would require a lot of trial and error and, as far as I know, has never been attempted. Also, I would advise against playing Ingress while driving.

There's an idea anyway that has been floating around, that I've found matches quite well my observations on the field: it's not exactly a matter of speed, but of radius around your last action. I'll try to explain this better:

Everytime you do an action in game, an invisible circle begins expanding from your current location, moving at the still currently undisclosed speed limit. Any other action done inside this radius, indipendently from your speed, will succeed. Any action done outside of that radius will fail. My experience, as I've said, seems to give strength to this theory, but I have only a very small sample to say it's surely like this.

TLDR: YMMV, but stay under 30 mph for best results.

Nobody but Niantic really knows the answer. It is most likely 30-35 mph, but even that limit is inconsistent, as it seems that some actions occasionally succeed while over the limit, and others fail under the limit. For example, rapidly spamming actions can be effective even well above the speed limit. One theory is that there may be a race condition such that an action is normally validated against the location of the last valid action, but instead, the location of the immediately previous action may be used if it had not yet been invalidated. On the other end, another theory for the fuzzy speed limit may have to do with the latency between when we initiate the action on the client and when it is timestamped on the server. The server may register the action even after we seem to receive a response from it (e.g., items, AP). If there is a long delay on one action then a shorter delay on a later action, you will have appeared to move faster and be incorrectly speed limited.

My experienced limit is a speed of about 50km/h.
Under this speed, I can hack portals as they are reached, preventing I have a good GPS connection.

But I have also experienced, that it can happen that my scanner blocks in an area where I don't have GPS anymore (for instance in a tunnel, or in a train where no sight contact to the satellite is possible). Then if I'm lucky, I can act on a portal (hack, fire, ... as long as I don't try to link to another portal). I made this experience on a distance of a few km.

So the speed is really linked to the GPS.

Here I have to say, that if I deactivate the GPS on purpose, while I'm on my way, the scanner uses other ways to locate me, so it does not work the same as if I were in a tunnel.