Not really. First of all, there is only one Signal client allowed to connect to Signal’s servers. And in the real world, the vast majority of Signal uses are getting their APK for that app from the Google Play store (the Signal team has said that they prefer you to use the Play store as well, instead of direct-downloading an APK from their website which they offer only grudgingly). That means that a state-level actor could possibly carry out a targeted attack to replace the Signal app on a given person's phone with a malicious build.
Also, Signal’s reproducible build system requires a specific version of the Android development kit. It has been pointed out that a state-level actor could be sitting on vulnerabilities in that, and not in the Signal source code itself.
If the attack is on the android dev kit, but not on signal, then.. the attack isn't on Signal, it's on the dev kit. Unless Signal's using an unusual version of the dev kit, your risk exposure to this attack is equal to any other app that you would use instead of Signal.
No, they couldn't. They would need the Signal developers' key. Android requires app updates to be signed with the same key as the original app.
That isn't to say "all crypto is hopeless", simply that you shouldn't consider Signal to be state-level actor proof.
That's all a smoke screen. Nobody is running an open client with a reproducible build, everybody is running whatever version is downloaded from their app store of choice.
It's not special, and I don't trust it a bit.
I submit that there is no better option right now.