Can we use the present continuous like this (in both languages)? And if it's currently May?
Yes, the present continuous can be used to express future plans in both languages.
Why is it progressive tense? Ans what is the difference from वह अप्रैल में जाएंगी?
वह अप्रैल में जाएंगी is future tense, not continuous:
She will go in April.