1. If I activated my card on 20/6 and used it straight away, do I need to pay the bill at the end of June or later on 20/7?
Check your statement date. You pay 20 days later (after statement date)
Eg.
Statement date: 1st of every month
Payment due date: 20th of every month

2. Do they notified you to make payment or if you have outstanding balance or you need to check by yourself at the end of payment period?
HSBC will SMS to you when you have outstanding balance.
At the end of the day you still need to go to www.hsbc.com.my to check
3. Can I pay the bill using other bank apps such as maybank app?
If your bills refer to TNB, Syabas, et cetera,
AND you were to pay using www.hsbc.com.my
You need to have security device.

Refer to my post Post #3970
https://forum.lowyat.net/topic/3457783/+3960