Confused About Notice Period and Leave: How Should I Resign Without a Confirmation Letter?

Need some expert advice, I'm currently employed for the past 1.3 years in this company. I don't have a confirmation letter given by the company all this time. I only have my appointment letter that states to give 7 days' notice before resignation.

My question:

I would like to resign from this company as I need to join my new company on 15th June:

1. Do I only give 7 days' notice as stated in my appointment letter, or do I still need to give at least a 2-month notice?
2. If 7 days is sufficient, does it include weekends as well? Does the day I tender my resignation count as well?
3. Can I use my remaining annual leave entitlement for the year to offset the notice period even though it's only May now?
4. Can HR force me to serve a 2-month notice at least (as this is what happened to my previous colleague even though there's no confirmation letter stating this)? Can HR reject my resignation letter?

Thanks a lot!

Notice Period Requirements

1. You need to give only 7 days' notice as stated in the appointment letter.

2. Seven days is sufficient; it means seven working days and does not include weekends, although it is not defined anywhere in the statute. The day you tender your resignation is not included.

3. You can use the balance of annual leave entitlement in proportion for the part of the year so far to offset the shortage in the notice period.

4. HR is likely to force you to serve a 2-month notice, but you need to stress the fact that there is no other communication addressed to you either confirming you in service or extending your notice period to two months. Unless these are specifically communicated, no presumption or assumption could be made. You need to softly challenge the HR Department that legally there cannot be any claim for a two-month notice, and you will not be cowed down. If HR rejects your resignation, in that case, issue them a proper legal notice.