Chirality Questions - Need Answers Checked

[FlipStyle1308]

I had to answer true or false for the following five questions. If they were false, I had to explain why.

1. In some cases, constitutional isomers are chiral. TRUE
2. Every chiral compound has a diastereomer. TRUE
3. Some diastereomers have mirror-image relationship. FALSE
Diastereomers are not mirror images of each other.
4. If a structure has no plane of symmetry it is chiral. TRUE
5. If a compound has a diastereomer it must be chiral. FALSE
Compounds without a chiral center (like an sp2 hybridized molecule) can have a diastereomer.

So I need to know if my answers are correct. If not, why are my answers (if any) incorrect? Thanks.

 

[Bystander]

Skimming your answers, no guarantee, but they look good.