Can I cancel my work permit a few days before it expires, and do I need to leave Thailand on the exact expiry date?

So generally here is what you do:

Get a letter from your employer stating your last day of work. About a week before this date you go and get your work permit cancelled using this letter. Then you take this letter and your cancelled work permit the immigration office that issued your work extension (it must say "extension of stay", not a visa, you cannot cancel a visa).

Immigration will cancel your extension and then stamp you in until the date on the letter you provided. You will not receive any extra time beyond this date, and definitely won't receive any extra time beyond the end of your extension.

*If you work for a BOI company, they have different rules and you will get between 7-30 extra days. No one really knows how they decide how many extra days you get.