At some point, the communication has to enter the terrestrial network. That entry node is likely to be under the influence, if not outright control, of Five Eyes security infrastructure.
You would need to build out a lot of infrastructure to escape the sort of ubiquitous surveillance that is available to those organizations.
Not necessarily. If you're communicating between two SpaceX terminals, that could feasibly avoid SpaceX ground stations. I don't know how capable SpaceX's routing actually is to know if this is within their scope though.
If it's flying through the air and somebody really wants to grab it they will, whether they can read it depends on how good your crypto is.
LEO is far from a true vacuum. But it's sparse enough that you have limited beam scattering. Getting a read on a sat-to-sat laser emission from the ground is nontrivial.
That said, I imagine that for any serious bandwidth, you won't get enough SNR to decode anything from the ground.
I guess if you got an observation platform up closer that would help.
If they were strongly encrypted there may be no reason for a nation state to observe the intersatellite links, but I wouldn't expect this at least for the near future since Elon's focus will probably be to cut corners to get the absolute best performance possible.
[0] https://en.wikipedia.org/wiki/Consultative_Committee_for_Spa...
[1] https://www.google.com/search?q=ccsds+protocols&source=lnms&...
Edited to add: I'm not making any claims on what protocols Starlink uses specifically. Just describing the general approach.
In practical terms I don't think it's a major concern. Much more likely that the spy agencies would tap the lines coming out of the ground stations.
Which is a significant step backwards for e.g. Russia.
Currently, all data between Asia and North America runs on cables. Anybody can spy on those. If those data did satellite laser hops, only those with ground stations would have access. Everyone else gets locked out.
I have no doubt that (like every other geo-mobile satellite constellation) the system allows for "port mirroring" on point-to-point links, or (more likely) relays everything through a ground station even when doing so has performance implications. This allows them to fulfill their obligation to government(s) surveillance.