You've identified the general region in the sentence where the error occurs; but not the error, or the correction, or the reason it might have occurred, or how you could correct students.
I will do the first one for you.
1-I am going to supermarket, do you need anything?
Correction: I am going to the supermarket. Do you need anything?
Reason for error:
the - the student might not have a native language that uses articles. It is therefore a common error to omit them.
. Do: This is a comma splice. Again, this might be possible in the L1, but is not right in English. (You can't join two sentences with a comma).
How to correct:
the: teach articles.
, Do: teach English sentence form.
Your turn.
Thanks for your help!
Regarding your analysis of the first sentence and how to correct the speakers'errors, I think that the speaker should be taught the punctuation marks instead of the English sentence form.
Here are my own analysis of the other sentences.
2-You don't have(don't need to) to finish that now if you haven't got time.
The reason for this is that the students is not aware of the difference between' mustn't' and 'don't have to'
Mustn't is used to say it is wrong to do things, or to tell people not to do things.
Don't have to is used to say that something is unnecessary.
3- I did a lot of homework last night.
This error might be beceause of overgeneralisation. The students might think that ' a lot of' is always followed by a plural noun, and homework is noncountable, so we can't add an's' to it.
4- I am bored. Can we do anything else?
The speaker can't distinguish between'bored' and 'boring'
Bored refers to someone suffered from boredom, but boring refers to someone or something that causes bordom.
