Very sorry to hear about your situation, OP. But you sound reasonable and that's always good first sign for moving on.
First off, are you wanting sole custody? Is that your primary concern?
If so, I think Singapore might be more inclined to grant that. I get the impression Singapore favors the mother for a young child's needs. If you file in Australia, it's likely more in favour of your (ex) husband since he's Australian, and you're not. Also, he's likely to have more contacts that you groping in the dark because you'd also need an Australian lawyer.
I need some clarifications:-
1) Under Australia Law, will I lose the custody of the child? What are the reasons which will lead to me losing the custody of the child?
I don't know about Aust law, but it's likely joint-custody. For some reason, judges and courts think this is a feasible healthy option which will not produce psychological basket cases. I wonder, because if parents were so on the same page in the first place and able to communicate well, why would they head for divorce?
If the parents have different parenting styles, cannot communicate, agree or compromise, and have other vested interests in wanting custody, this arrangement is a doomed failure.
2) I do not want anything from the father as I am a working mum. Does he still need to pay for child support and alimony?
Alimony is for you. That is your choice to take, or not take.
Child support is something he should be paying, as this is his duty as a responsible father. Whether it will be regularly consistent on not, is really up to the individual's conscience and sense of committed responsibility.
An example: circumstances change, he may meet someone else, and this monetary may be seen a burden.
Though really if you really want sole custody and to be "hassle-free". taking his money can be a tussle between you and a source of control leverage for the father. It really depends on whether he sincerely cares for this child, or if custody is really a masked power struggle. In that case, make a clean break. It's much easier for parenting and your future sanity.
3) Currently he is trying to apply AUS passport for the baby who has a SG passport. Do I need to sign on those documents? Can I refuse to sign?
Ever ask WHY? (I think you have a right to refuse to sign).
SG is more likely to favor you legally. As a Singapore citizen, and because your male child holds the SG passport too. Australia is more likely to be interested in protecting this child, once he holds an Australian passport. Do you really want to go there?
4) He has a house in Aus and my lawyer said if he were to apply divorce under the Aus Law, I can claim the house or half of what it's worth and keep it for child's education. Is this possible? And take too long as I want it to be as hassle-free divorce as possible.
If you want a "hassle-free" quick divorce, and you're entirely financially independent yourself, I'd say don't bother fighting for his house. But, it's not a lost cause. You can use this as leverage for negotitiation.
If his assets matter more to him, he may be willing to give up custody rights to his child. You can opt not to sue for half his assets and ask him
(in writing) to give up all rights to joint custody. In return, negotiate. People are more likely to buy in, if the deal is sweet for them too. Perhaps you'd be willing for holiday visitations for your child to Australia, on his expense?
Best of Luck. Only you know who you're dealing with. Above are my opinions only.
Also, a word of caution. are you certain your (ex) husband will not come on this board? Your cards are transparently displayed when you ask your questions here on a public forum.
Grab a good lawyer who is not just educated in local Singapore law. Know what you stand to gain by filing in Singapore vs Australia. Know what you're willing to give up.
Also, learn to read between the lines when advice is dispensed. Be aware of the lawyer's own self-serving agenda. As POD has mentioned, a divorce lawyer's bottom-line is really his fees and what he stands to gain with easy resolution vs trial. It's not about ethics or doling justice. They're good at sizing up how much there is at stake in the honey pot.
It's like buying a house, with multiple competitors. As with house buying, divorce is a situation which plays on emotions, reactions and vulnerablity. If you do not stay wise, calm and rational; with pot-stirring lawyers playing with emotions and reactions on both sides, a simple process can escalate into a complicated circus.
