1. The email is from Diana. - F (The email is from Emma.)
2. Emma likes her new neighbourhood. - T (The email states: "My new neighbourhood is great.")
3. There are not many shops. - F (The email states: "There are lots of shops and cafes.")
4. There is a sports shop near her house. - T (The email states: "I even have a sports shop right opposite my house!")
5. There's a library in the neighbourhood. - T (The email states: "There is also a library next to the supermarket.")
6. Diana can stay at Emma's new house. - F (Emma invites Diana to stay with her during the school holidays, implying Diana would stay at Emma's house, but the sentence is about Diana staying at Emma's *new* house, which isn't specified.)