The statutory declaration is merely granting the company permission to verify your background. If they actually spend the time to run the background check, that means you've got a high chance in getting the position. As usual, don't count your chickens before they hatch, because nothing is certain till you actually receive an official offer. Don't think so much and continue with your job hunt until you hear from them again (to which you can always drop them a courtesy note to check if no news from them in about 1 week or so).

Depending on your situation (e.g. fresh grad vs long time worker or have had multiple holdings or seats as directors), the background check can take from 3 days to 3 weeks.

As mentioned above, the statutory document means that you are stating that what you have submitted is the truth. There was once where I made a typo in the year of my previous employment history in the resume but it didn't match with the statutory document. The bank called back to verify it and I had to make sure and provide the proof of employment during that time.

You only get the job offer when you literally have the job offer in hand (physical document or soft copy), which is the employment contract.

Yes, when I made the mistake, I went back to change the necessary documents, SD, commissioner of oaths and then resubmit and the process started again. It was quicker the other way around as they had already initiated the other checks (e.g. credit, bankruptcy, legal litigations, police, etc..)

About 3 times as I have gone through 3 different companies which requires a background check (2 financial services and 1 tech). Fastest taking 2 weeks, longest taking 4 weeks. All 3 resulted with a job offer with the exception of one where the job offer was given first prior to the background check.