Do your parents know how hard you’re finding school? There might be some more supports or more specialized ways the teacher could approach your assignments or instruction time/style. I have a son in Grade 3 who is struggling much the way you are, and I really empathize with you. It must be very frustrating when the way things are being taught is not a good fit for your learning style. I hope you find some ways to keep up – an ADHD coach might also have some ideas.
For the apology letter – I can understand the desire to explain things to people, however I can also see how your letter could be interpreted as excusing unacceptable behaviour, and I would be very careful to make sure you’re taking responsibility for your behaviours and how they affect others. There’s a social contract (for example with the hugging you mentioned) that we don’t hug people who don’t want to be touched, and that we stop when someone asks us to stop. If you’re breaking that social contract, you need to take responsibility for your actions, instead of asking the other person to accept behaviour that they find unacceptable. If you don’t take responsibility and find a way to manage your behaviours, it could eventually get you in a lot more trouble than just losing friends. Also, an apology should be focused on letting the recipient know that you’re aware that what you did was wrong/uncomfortable, without making an excuse, and it should offer some amends. Otherwise, I fear your letter will come off as offensive as well.
I hope this doesn’t come off as harsh, but I’m a parent of an ADHD child and I would never want him to send people a letter that excuses his hurtful behaviour, or puts responsibility on the victim to change their reaction or learn his “trigger words”. It’s up to every person to manage their own behaviour, and accept the consequences when they’ve crossed someone else’s line. Every person has the right to be respected, and ADHD is not a free pass to disrespect other people’s boundaries.
The great thing is that you’re young enough to learn some new skills, learn what things other people find offensive or what breaks the social rules we’re all trying to live by, and figure out strategies to help you follow those rules. I would put my energy into that, as well as offering a genuine apology if you’ve crossed someone’s line. Remember that to them, it probably doesn’t matter WHY you crossed the line, but it will matter to them if you accept responsibility for how you made them feel, and offer to make amends. That shows you’re a caring person, which I’m sure you are!