Q.1 how and why did Max came inside ausables room??
Q.2 what made the story of balcony so convincing??

Dear Student,
Given below is the answer to your question.
 

1. Max entered Ausable's room using a passkey that he got in the absence of Ausable.He had come stealthily into Ausable’s room and wanted the report on the missiles.
2. Ausable created a convincing story about the presence of a balcony. He said that twice in a month somebody had entered his room through the balcony. On being questioned by Max about the balcony, he replied with extreme irritation that it was not his balcony. This reaction, which looked natural, played a part in convincing Max. He further told Max explanatorily that his room was earlier a part of a larger unit and the adjoining room was the one which had the balcony. He said that it extended under his window. His manner of description and speaking convinced Max that there was indeed a balcony under his window.