Were you staying together during the marriage? You have to realise that a man has his limits. If you don't live with him nor consummate the marriage, he may just leave you when he gives up waiting. You have a marriage certificate. Your marriage vows and obligations stated in the Women's Charter are clear: Put the marriage first. Cooperate with husband to safeguard the interests of the marriage. That includes intimacy as well.
What are your priorities? If you want your career at the expense of marriage, just sign the annulment and move on. You can't keep a man around and not fulfil your wifely duties. It is grossly unfair to him, and very selfish. Can't expect miracles to happen when a couple lives apart most of the time. Perhaps the time apart will give both of you time to think about your priorities in life.
1) If you don't agree, he can still file for separation, which will come into effect as divorce 3 years later with your approval, 4 years without your approval. Heard of a case where a woman asked her ex to separate instead of divorce so she could keep the flat to herself while dating a new guy.
2) Not sure.
3) I think you can go for counselling first before you decide what to do. Perhaps the love is still there, but he may think you put him in last place. Can't expect a marriage to work if both parties do not put each others in first place.
4) HDB will act based on court order, which comes after the Final Judgement. You can settle amicably and appeal to HDB to sell on open market if MOP is not met. Otherwise, it may have to be surrendered to HDB and you get only money based on current valuation.
In summary, go for marriage counselling and try to repair this marriage. Stay open minded to suggestions and feedback, and make a sincere attempt to save your marriage.