Do tax payers under the composition scheme also need to file GSTR-1 and GSTR-2?

No. Composition tax payers do not need to file any
statement of outward or inward supplies. They have to
file a quarterly return in Form GSTR-4 by the 1st of the
month after the end of the quarter. Since they are not
eligible for any input tax credit, there is no relevance
of GSTR-2 for them and since they do not pass on any
credit to their recipients, there is no relevance of GSTR-1
for them. In their return, they have to declare summary
details of their outward supplies along with the details
of tax payment. They also have to give details of their
purchases in their quarterly return itself, most of which
will be auto populated.