I have experience with this seat (Cosco Scenera) both forward- and rear-facing, both in cars and on planes.
1. The installation guidelines for cars apply to planes, too. The FAA requires these guidelines to be followed in both vehicle types. So weight limits, belt paths, whether the "kickstand" is up or down, etc. all should be followed in planes just as they are in cars. This means that a 7-month-old should be rear-facing on planes in a Cosco Scenera. (I say should.)
2. The Scenera does fit rear-facing on planes. I've installed it in a wide variety of planes, including commuter jets, just fine.
3. Some US flight attendants get confused when they see any seat other than the bucket-type infant carries installed rear-facing, and there have been reports of passengers being asked to turn convertible-style seats around to forward-facing, even if the installation instructions are clear that it should be installed rear-facing, given the parameters (child size/age, etc). The FAA guidelines are a little ambiguous, and less experienced flight attendants misinterpret them sometimes. This isn't directly relevant here, since Singapore's guidelines, according to your research, prohibit rear-facing carseats outright.
4. All this being said, you could turn the seat around to forward-facing and put your 7-month-old in it. It will not be reclined at the appropriate angle for a child that age -- and the seat does sit pretty upright when forward-facing, so expect his head to flop forward when sleeping. trying to support the head on the sides with rolled up blankets or whatever doesn't work so well. I have tried. Practical experience here. Even rear-facing, there is some head flop in this seat, but you have a better shot at stabilizing it with a blanket at that angle.
5. Check out
http://car-seat.org to see if they have any insight.
6. I think you may be stuck forward facing it. But maybe if you're in a bulkhead, you could try rear-facing it in the window seat? The flight attendants may not say anything. If they do, then you could then turn it around. I'm assuming, here, that the reason the airline doesn't allow it is that RF seats can impose on the passenger in front of them, since they will not be able to recline their seat. If you are in a bulkhead seat, this point would be moot.
7. I'm not sure why I'm numbering everything.