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...
Doesn't sound like a great start to securing your system.