I heard back in 2 days with a proposed salary range.

I think every employers have different timelines. It can be days, weeks or months as I have seen in this thread.

Any news on this ?

Is it normal for HR to ask for your latest payslip (compulsory) before the interview?

I think it's normal. Encountered twice.

How to sense if the hiring manager would like to hire you?
If they talked with you like 1 hour, manrtioned you OK, in the end said wait HR, within 2 weeks.

Will HR inform me if I'm not selected?

The government sector appears to punish those who make any mistake in their career. I joined a stat board at the start of this year but it turns out to be the wrong job fit and went to apply for jobs after 3 months. Every interview the panel will say I job hop even after I explained the reason for looking out and reject me. Like that is no one allowed to make a mistake? Then they have to suffer at the wrong company for how many more months or years then is more politically correct to look again?

if i am asked to do a health questionnaire, does it mean high chance of getting offered?

They always inform me if I am rejected after interview.

Obviously for your case, the HR thinks you could be a good fit hence you are invited for the interview.

However, it is the actualy department who rejected you.

I would say not all departments are like that, and you should keep trying.

Good luck and god speed.