First of all our congretulations Les. I am really happy for you. Think you will like it there.
Now you can start applying for a Tiger Airlines frequent flyer pass for your cheap flight to LOS.
Yes Coolhand is right for Singapore. She needs to show, she has enough funds. Alternatively, you could bring Nee in yourself. To my knowledge 30 days is the mx they can stay without visa, but I do not know what are the minim intervals between visits. I am sure there is a decent Singapore website informing you about that.
Anyway, I hope you will have a great time there and let me know in which area of town you will get your appartment.