Hi Elena! I will try my best with the equivalents in direct speech - We insisted on them staying for dinner. "Please stay for dinner!" She apologised for forgetting my birthday. "I'm sorry I forgot your birthday." He accused her of stealing his wallet. "You stole my wallet!" He agreed to help me organise the party. "I will help you to organize the party." They warned the children to stay away from the water. "Children, stay away from the water." Here's a good article about the "verb shift" used with many tenses when you change direct speech to reported speech: http://www.edufind.com/english/grammar/reported_speech.php

These are already in reported speech. Did you mean direct speech?