Yes, I see red flags. The first is that even if you share joint custody, the two of you aren't together anymore. Thus ends any obligation to please him or to discuss in that language. You two are now only business partners, and have to remain professional. No more personal crap.
The second is that his continued communicating to you every little thing sounds to me like he's not letting go of your connection or relationship, whatever that has been. I've known this at close range and it's unnerving and obnoxious.
You probably can't change any of his communication style; only your own. I would set about ignoring the hell out of communications like the ones you've described, and try not to take them personally.
Re: 1. You're a good parent and you know what you're doing. The deal after a breakup or divorce is that each parent gets to do things their own way. I admit I would probably respond with that at least once: "I appreciate your ask, but will continue to do what feels most reasonable to me. You're welcome to do the same." Let your kid decide. As he gets older, he will, and let him know it is ok for him to stand up for what he wants.
Re: 2. As a parent and an adult, this joker can dial the phone himself. His asking you for information here is a little obnoxious, especially with the "please me" statement.
If you are primary parent or if there is any high conflict potential here, provide the father with ALL of the emergency and medical/dental contact or insurance information he needs, ONCE. Send it in email and if he needs other things like vaccination record etc. he can go about getting those records directly from hospital or physician. I keep my ex apprised of all health appointments I make it take our child to. But if you are in high conflict and he seems to be doing a power play or a series of them, keep your communications concise and devoid of emotional content. I would consider telling him you got rid of text messaging, and to stick to emails. That way you're not triggered every time he pings you. Wait 24 hours before responding to anything, unless it's clearly emergency. If he's N or PD, he may occasionally fabricate one just to get you to respond. So much fun.
Re: 3. He regrets, and he enjoys. This is bullshit you do not even want to discuss. Who cares what he feels? If you do, or if you are using this same type of "feeling" language, stop. If you stop and he keeps on, he's still vested in you emotionally. Having watched this too long in my own life, I'm warning here that this is not good. The last thing you want is to drag out the emotional connection. Whoever broke away from who, let them go. Cut that cord as completely as you are able. Otherwise it is endless, sorrowing, and periodically abusive.
It's hard to know exactly what you're dealing with, from this post, but if you are done with this guy, be done and don't feel too bad about it. If we broke off or are perceived as the parent with the most power or information, I do think we must be fair in giving the other parent equal opportunity to be as good a parent. This means sharing business information. Not telling stories about what you do with the child, or how you feel about it, or telling the other parent how to run their side of the business.
He shouldn't be, and that he is makes me think he hasn't got the full understanding yet that the two of you are through.