My year one child is struggling with maths and handwriting
I don't think this is a major thing, honestly, i think that your child is still finding his own way. Some children may not be that interested in maths or handwriting. This is not uncommon with kids of this age. It might be that your child just didn't understand what to do from the teacher he had. The same goes with handwriting.
I know its sounds silly but try and get your child to do maths work without knowing he's doing it.
You can use maths to get a reward, for example, "Tell me the answer to this question and you can watch lego Ninjago". Be careful though as it can backfire on you.
You can cook something or make cakes and use the weighing as maths. You can also reward by giving a treat at the end of it too.
Use the internet and apps, there's loads of stuff out there.
With handwriting try and get your child to write whenever and on what ever. Dirty cars, spell with food, leave funny messages around the house for you to find. Really get into it, the funnier you find it the better response you will
My kid’s teacher accused my child of hitting another child, however i don’t believe my child did anything
It sounds to me that a child had been hurt and your child got caught in the crossfire.
I suggest that you speak further with your child's teacher and explain your concerns on the matter. Try to come up with some kind of way you can move forward together in a way that mutually benefits all parties involved.
If you honestly believe your child didn't do anything then you should stick with it. If the school haven't any solid evidence then there isn't much they can do as far as getting your child in trouble. The school may, however, keep an eye on the situation with the children involved. This isn't a bad thing as the school can now be more aware.
Have a chat with your child about staying away from bad behavior.
My 7 year old son is overly concerned by other kids behaviour (they are hugely disruptive)
This is a good thing, it is showing that your knows right from wrong. Unfortunately, there are always naughty kids in what ever school and it's just something that your child will, and is, coming to terms with. In the mean time just be happy your child is not one of those naughty kids.
My daughter (6 years) seems to get held back with reading and spellings
All you can do is promote reading and spelling as best you can. Reading with your child in the night is always good. Try to get your child to help you with things like making the dinner. Get your child to read the instructions on how to cook the meal (basically dumb it down a little).
Like I said before its all about getting him to do stuff without him knowing he is doing it.
I don’t like the language and tone my younger daughter (8) uses.
Children use slang terms when they are younger, it gives children an identity and helps to make friends. I know it sounds very alien to hear words and sometimes the things children say may not be appropriate.
Don't be afraid to confront your child.
With these issues, if you have a problem then say you have a problem. Remember you are the parent but keep in mind that you probably had your own language with your friends when you were younger so try not to be too harsh.