Can I delete emails from my iphone without them being deleted from my laptop?

It depends on the type of email account that you have. This is simple with a POP account, however if you have an IMAP or Exchange account, they sync via the server, and if you delete something in one place, it gets deleted in the other.

if your email account is using IMAP (gmail icloud outlook and other providers all use this) protocol than no, you will want to move the messages to a different folder instead of deleting or enable so it archives instead of deleting in advanced mail contacts and calandar settings