Obviously it’s important to dress formally to an interview, but how do you know exactly how formally?
There are a few different theories for this. I subscribe to the theory that suggests you can't be overdressed, and unless communicated beforehand that a different style is more appropriate I wear a suit and tie.
If the point of dressing for an interview is to convey you would fit in with the culture, wouldn’t it be possible to over dress?
If that were the point, then yes.
However I believe the point is to present yourself in the best light, and under-dressing will always harm you more than overdressing, so if there's uncertainty I suggest you be overdressed.
Keep in mind that you're being compared to all the others applying for the job, and if your dress is less, even though it mey not bear on your job it will leave a negative impression compared to others.
Consider two stores - one is freshly redesigned, painted, well maintained, and brightly lit, while the other is adequately lit, adequately maintained, and has a usable design. You'll find that most people prefer the nicer one over the other even if in all other aspects there's no real difference other than looks.
Should I have mentioned this or apologized?
If you have to yawn more than once during an important interview, then you're already displaying an inability to prepare for an important meeting and present yourself rested and ready to work and interact. This coupled with leaning back suggests a lack of interest or desire to "win" the interview.
If you have a reasonable explanation that tells them this was unavoidable, exceptional, and will not happen in the future when you are working for them, then, at this point, it can't hurt you more than your yawning and slouching already have to try to explain your condition.
In other words it probably doesn't matter, you've lost the opportunity, so an explanation can't hurt, and may possibly help if you can convince them it's unusual and wouldn't happen again.
If you do feel the need to yawn in an interview, what should you do?
Take deep breaths. Try to focus on what's going on. Pinch yourself surreptitiously, bite your tongue, dig your nails into your palms, or do something to get your body to be attentive without alerting the interviewer that you're having a hard time controlling your body.
If you have to yawn, make it as small and short as possible, cover your mouth, don't stretch, and while you should look away from the interviewer, don't point your head towards the ceiling or use any more movement than necessary to regain control after the yawn.
Apologize without explanation and move on, "Sorry. So your questions was..."
He also said I stretched my arms but I don’t consider this rude?
It's not rude in some contexts, but, like yawning, it shows a lack of either preparation, or control over your body. Perhaps neither should or would affect your ability to perform, but body language is tricky and it may be interpreted as lack of attention or care for the proceedings.
Should I chock it up to bad luck?
No. You should alter your behavior and preparation for future interviews.
Should I email the recruiter and say I disagree with some of these points?
Your recruiter is interested in finding you a job, and by getting feedback and giving it to you they are trying to make you better fit the needs of the clients they are working for.
If you do not believe you did one or more of these things, then I suppose you could dispute them with the recruiter, but what effect will that actually have? Maybe they believe you and they move on. Maybe they believe the interviewer and start thinking of you as unaware - or worse, a liar.
It might be wise to respond to the recruiter saying, "I appreciate the feedback and will prepare myself and present myself better next time."
Then do so.
Should I assume the recruiter doesn’t want to work with me anymore?
I wouldn't assume anything. If they don't doubt your technical skills, they'll probably continue to shop you around.
Call or email them and ask them 1) if they have any other positions that might fit your skills, and 2) what skills employers are looking for in this area that are close but don't exactly fit your resume.
This will show them you're interested, you're able to adapt, and the simple act of following up will demonstrate you're motivated, suggesting that you'll work to improve how you present yourself.
Should I email the HR rep and apologize?
No. Your business with them is finished, and if you don't want to annoy your recruiter don't attempt further contact with the company. Remember, your recruiter may still be trying to fill this job and get the recruitment fee - so they still need to maintain a good relationship with this HR.
FWIW the HR rep offered me his card before I asked and find this strange given the way he felt about me.
This is automatic - even if they didn't like you they will still act professionally and give you contact information.
Even if others are correct and this job isn't good for you, receiving the offer and having the choice to accept or reject it is better than not receiving the offer and having no choice. Assessing whether a job or company fits your requirements and has a culture you're comfortable working in is another question entirely, and while it's nice to pretend that you've dodged a bullet, it's not the best result possible, and the things you can fix are easy to fix so there's no good reason not to.