why "this" instead of "the" is not accepted?
"this woman eats cheese" would be more likely translated to "Tato žena jí sýr".
"Ta" is used mostly as "that", or "the".
and why not also 'the/that woman eats cheese'
that is accepted
I just used that and it wasnt accepted. 'that woman is eating cheese'
It is accepted. To report missing translations use the "My answer should have been accepted" flag to report missing translations, not this discussion. Check for typos first.
The woman eats cheese. The woman is eating chesse. Where is the different or mistake?
Both are possible.
Why do they use ji instead of jedi or jis
Based on all your last questions you really need to have a look at the Tips and notes provided. The verb must agree with the subject. jí is third person singular, jedí is third person plural, jíš is second person singular