There are many diving schools and operators in Singapore. Just do a google search and you will find many. There is an instructor by the name of Spencer at Costa Sands who teaches very very well but his course fee, very steep. But your foundation would be solid if you are coached under him.
Actually neither can my wife! But we dive regularly. It's become one of things we look forward to doing as a couple. You'll be surprised after getting married, both have so little in common.
I can also recommend you a wonderful dive instructor. Not so long ago, I was afraid of the sea. I nearly drowned as a kid and had this phobia ever since. But this guy was so patient and skilled. I jumped into the open waters and never looked back. In fact by my second dive trip, I bought a few k worth of dive equipment for the long term.
I think the 200m swim and 10 mins of treading is meant to see if you are ok in the water. My suggestion is that you should go for a scuba tryout before commiting to attending a course (as the course will cost you more than S$400) and see if you are really comfortable with scuba diving.
Hope you have fun diving. I just came back from my first dive trip after a break for abt 4 years and it was quite fun.
swiftdragon, yep. I guess they just want to make sure you are comfortable in the water. Can you even swim at all? I could swim 1 lap, but can't tread water for nuts. Nowadays I am better at it, because I've been practising in the pool at my place. I guess swimming is the most basic skill to save your life.
Oh BTW. I would advice you to find a good instructor, rather then find a cheap deal. There are some dive centers out there who will take you for peanuts, with substandard instructors and cockroach infested boats. Ultimately, these instructors will be imparting knowledge and skills so you don't kill yourself, instead you will have a good time once you know what you are doing.
I am sure many of the sunburnt oldies here have seen divers with such bad fundamentals, they risk themselves and everybody else around them.