I would like to ask two related questions:
How can we encourage a child who is in 3rd grade with ADHD/ADD to do his own homework without relying on his mom?
How can we teach him to behave more calmly, to listen to and be more respectful of others?
I've referred to my own answers a lot in this Answer. That's somewhat because there are a lot of people with similar concerns, and it's come up before. It's also because I have an ADHD son, and we've tried a number of things that did and didn't work. But I am not going to claim I'm the only expert out there: plenty of perspectives and ideas are available. Look for those other resources too, as you continue to learn more about your son's behavior and what works (and doesn't) for your family.
Read a lot. ADHD has a multitude of symptoms, and not all children have all symptoms; advice that works wonderfully for one child may be useless for another. Be willing to try a variety of approaches, keeping what works and discarding what does not. (Much of the advice is useful whether a child has ADHD or not!)
Consider professional help. I've gotten lots of advice and ideas from other parents and the internet, but we also work with professionals. His pediatrician is our primary point of contact, and has referred us to other specialists for diagnoses, therapy, and counseling. If you're uncomfortable or disagree with their opinions, ask questions or push back: as a parent, you know your child best.
I recently gave another answer about helping with homework, advice that can work with either an ADHD or neurotypical child. I suggest reading through all that, but here are some of the highlights:
I also suggest establishing a schedule (homework is done when you get home, right after your snack and before play time), and emphasize that you believe he can do this. If he hates homework as much as my son, there will be lots of arguing and excuses at first. ("I can't do this", "I don't want to", "I'll do it later", etc.) Calmly refuse to accept all of that: he needs to sit down for his homework now, and he is capable of doing it, and if he has any questions about the content you are happy to help, but he has to attempt it himself first.
Finally, when you set up a structured schedule and help organize big tasks ("homework") into smaller ones ("reading", "math", etc.), describe why you're doing this. You understand he finds this challenging, here is an idea that may make things easier. Not only does this acknowledge and accept his difficulty, but it provides lessons he can remember later in life (college, work) when you aren't there to guide him. ("Oh yeah, when I was overwhelmed by a big homework assignment my mom helped me break it into smaller jobs. Maybe it will help if I try that now with this overwhelming thing...")
It's an ongoing process, but it can and will get easier over time. Two years ago I never expected my son to get through his homework without a tantrum. Now -- it's regularly manageable, and sometimes even easy.
As for helping him be more calm and respectful, that can be more of a challenge depending on which particular ADHD symptoms your son tends to have. Keeping that in mind, I've got a couple other answers that you might want to read (about motivating a ten year old to take responsibility and helping a five year old who struggles to concentrate). Again, the highlights:
Concentrate on positive statements and praise. ADHD kids are almost constantly told how bad they are at paying attention and being calm. They can't meet expectations, and therefore conclude they are inherently flawed -- even though they just need to put in more effort. All that self-blame and low self-esteem can cascade into anger, depression, behavior problems, and an general attitude of "I'm not going to bother listening because all I ever get is criticism and scoldings."
You do need to provide guidelines and discipline, but look more for opportunities to strongly praise good behavior ("thanks for waiting patiently with me in the store!") and little successes ("good job finishing your homework today!"). Keep praise related to effort applied, not natural intelligence or skill. ADHD requires more work, and having that be recognized is rewarding.
Secondly, be willing to remind gently and repeatedly what expected behavior is or what needs to happen. Remove distractions if they're getting in the way (like a favorite book that's irresistible when he should be getting dressed). When he's starting to act up, calmly remind him to stop ("I need you to not run while we're in the store"). Sometimes, letting him know something's ending soon ("we'll be done shopping in a few minutes, I need three more things on the list") may be enough for that last burst of patience. In any case, though, calmly is very key: remind him of appropriate behavior, rather than scold him for inappropriate. Often, that persistent reminder can get him through a stressful experience that might otherwise lead to hyperactivity or a tantrum.
How can a child who is in 3rd grade with ADHD/ADD enforces himself to do his homework without relying on his mom?
1.) Be as sure as you can about the diagnosis.
I want to take a moment to tackle a difficult topic first. ADD is real, but there is a concern by many people that there are a number of false diagnoses for ADHD and ADD. You can read these articles for an overview (Michigan State University, Time Magazine). So, correctly addressing this reality with your son is very important to your questions.
2.) Understand the limits your son has
If your son has a real disability by definition that means he cannot stay focused on his own. The fact that he has ADHD means he needs help. Understand what his limits are. Help him learn to build stamina through exercises and skills which help focusing. I don't know what these are, but they can help him reach whatever level he is able to.
3.) Don't push him past his limit
This is obvious, but easy to overlook. We all want our children to be successful. It can be hard to accept limits when they apply to school, since learning is tied to success in our minds and our culture/society. For me it is more important my kids understand their strengths and weaknesses, learn to accept what they've been given (happily and joyfully!!) and in that context achieve all they can in life. I have three kids, and if one is a doctor, one a lawyer, and one a waitress I already know I'll be so proud of them all just the same if they are happy in their lives.
How to adjust his behavior to more calm, listen and respect others?
This ties back into number 2 above. There are skills and practice that needs to happen for him to learn and apply new behaviors. Being calm and listening may always be things he struggles with. That is just what ADHD is.
However, no matter what else may affect him respecting others is something he can do.
How you personally define that matters a lot. If your definition of respecting others is to sit still and pay attention with a solid steady gaze while they speak to you, then you already know he will struggle with that. On the other hand if your definition of respect is saying yes ma'am and yes sir then you have every reason to expect him to be able to do that.
As with all children and parents learning takes time, patience, and lots of consistent effort.