The idea that you can make an open / anti-surveillance device out of an iPhone does not seem likely to me. I was under the impression that you're stuck with Apple's proprietary firmware and OS regardless of what you do to the hardware.
You can jailbreak iOS if you want to run custom software. You can't be as certain that the device does not contain some remotely activatable backdoor as with free software (which does not mean you can't be certain at all; the whole premise of jailbreaking is that binaries are inspectable, and you can obviously sniff traffic coming from devices), but it would be somewhat odd for Apple to maintain such a backdoor at the same time it's getting the FBI pissed off at it for improving disk encryption (thwarting efforts to retrieve data from physically obtained phones). The baseband cannot DMA into main memory, last I checked, which at least mitigates a common concern.
Perhaps more importantly, I consider the whole issue of backdoors pretty moot (in a bad way), because every smartphone contains a web browser with many remotely exploitable vulnerabilities - that's just the way browsers work in 2015 - and it is not that hard to get someone to click on your link. If you're an intelligence agency, why would you even bother deploying a backdoor that could get you in trouble when you can accomplish the same thing through normal vulnerabilities?
By jailbreak you mean execute an unknown binary from a (probably?) untrustworthy website which exploits an unpatched local privilege escalation in the operating system, right?
Doesn't sound like a great start to securing your system.
Depends. The unpatched local privilege escalation is usually not remotely exploitable, and the initial entry point is typically over USB and requires getting past the USB pairing process (i.e. you need the passcode), so it shouldn't matter that much; in any case, the 'real' bad guys have 0-days, so it doesn't matter that much whether there is a non-0-day present.
As you say, there is then the potential risk from the jailbreaks themselves, which recently have all been Chinese (yeah, yeah). I don't think the real, practical risk of this is very high, as long as you ensure your binary is actually the same as everyone else's rather than some tampered item, but it exists. I do think jailbreaks should be open source; sadly I think there have been none since my last jailbreak, written back in 2011, and while a non-obfuscated binary is perhaps even better than source for analysis purposes in such a community (since analyzing the binary directly obviates the need for reproducible builds), jailbreak binaries have also recently been heavily obfuscated for no good reason. So there is definitely room for improvement, if anyone cares about this. isios7jailbrokenyet.com is still holding onto a $30k bounty for an open source jailbreak...
> I was under the impression that you're stuck with Apple's proprietary firmware and OS regardless of what you do to the hardware.
If the physical microphone is removed, the firmware and OS can no longer record ambient audio, unless an external microphone is attached. This would not create an "open / anti-surveillance device", but it would prevent remote audio surveillance.
If I'm incorrect here, I'd love to hear it.