It sounds like you have a great flexible opportunity lined up. If you have that much flexibility it really is up to you. Some people are more productive in the morning. Some are more productive in the afternoon.
In terms of full days or half days I think that too depends on you. I am a procrastinator, it's a terrible characteristic, but I seem to work best under pressure even if self imposed. I also work best with a good head of steam. It is not unusual for me to put things off and then pull a three day shift to finish a project.
So for me half days don't work. It takes me a little while to get a head of steam up but then I don't stop.
My experience (in a large MNC) is the same as DcKen. This Singapore work ethic is highly overblown. People aren't in until 9AM. They leave for lunch around 11:45 and don't get back till 2:00. They will work till about 6, I have noticed, and there are a few that stick around till 7 some nights. I have noticed there are also a few that seem to take as many sick days as they can. Even feigning a cough or something like grade school - weird.
My schedule is whacko. Sometimes I get in at 6:30, sometimes 10:00. Sometimes I finish at 3PM and sometimes I finish at 10PM. Many nights I am on the phone to the US and sometimes don't finish till 3AM. Sometimes I work from home. I never take more than 15 minutes for lunch. Almost always at my desk. Once in a while I will join an office lunch for appearances. Work is for work, why delay it with taking a lunch.
The ultimate flexible job. I can imagine what the locals say about me and my schedule.
One risk of working at home is being able to turn it off. I worked at home for quite a while in Malaysia. A fax would come in at midnight from teh US and I would go in the den and start working the problem. You gotta set limits.