The Golden Rule is as good a litmus test as any here - would you want to be secretly recorded? I certainly wouldn't. Recording someone without their consent violates their trust, if nothing else. Particularly when even one of the motives is to use the recording as evidence when they've said something you perceive as wrong.
2 out of 3 of your points are about your concerns that the company will in some way behave in a way that either compromises your rights or is directly opposed to your best interests. I'd offer the idea that starting an interview process with a company with the expectation that you are likely to be screwed over is probably about the worst way of preparing for an interview that I can think of - as Rachel points out, the non verbal cues can be as much a part of the interview as anything you can record on audio. There are some very distinct non-verbal cues when you distrust a situation and they often make a person appear untrustworthy. Unless you happen to be a phenomenal poker player, you'll have a tell.
On this one, I'd recommend two things:
If you want to improve your interviewing technique, get a friend or collegue to interview you and record it (on video) openly. For most people, the recording process will add to your nerves, mitigating any comfort you might have experienced from interviewing with someone you like and trust. Get their feedback and watch the video.
Then you're not breaching anyone's trust and you finding your own good pointers.
Performing artists do similarly quite frequently and with very good outcomes.
Address your Trust Concerns Other Ways
I generally approach an interview with a thought of "what's the worst that can happen?" The worst is really that I don't get the job. So what? There's a lot of jobs out there, and I can guarantee that fighting your way into making an organization hire you is not going to be nearly as good an outcome as finding a job that wanted to hire you in the first place.
You could say that the "worst" is that you will quit a good job and have the new, verbal offer retracted. But most people buffer this with actual paperwork. If you give me a verbal offer and I verbally accept - most sides will understand that the acceptance is still conditional on having a paper offer. Don't quit your job until you have the paper and we're back to the final outcome being that you still have the job you always had, you just don't have a new (on paper) job offer.
Of note, at least in US - a paper job offer will cover you for unemployment benefits if the paper offer is later retracted. I couldn't even hazard a guess whether a voice recording of a verbal offer would stand up to the same legal scrutiny.
In cases where the risk is low, I can always see my way to being a lot more trusting.