The Star of Temasek has never been awarded. Neither have the next two medals. Therefore, the protocol toward their bearers has not yet been fully established.
I suspect that even if it were not required, the current President would be happy to salute a bearer of the Star. President Nathan is a very humble man in person. He even has standing orders for guests not to rise when he enters as a guest of honour. I am happy to say that starting from Wee Kim Wee, all our presidents have been excellent chaps.
As for the Prime Minister saluting the bearer, that's a different story. However, given that the PM is a former general, and apparently a very caring one toward his men based on personal accounts, I suspect he would also be happy to salute a bearer of the Star. It would be good for morale in any case. SM would also probably be quite OK with saluting. He is not overly concerned with rank and is a nice guy. MM -- totally different story. Nobody can safely predict his actions.

The Medal of Valor has been awarded several times. I think it is the lowest military award for gallantry. The famous COL Lo Yong Poh got one for running around Kabul unarmed negotiating peace between the warlords for the UN, while the city was being heavily shelled by said warlords. Dodged a lot of shrapnel for peace. A few were given to the SOF troopers who resolved the SQ hijacking. A few were given for bravery during the NZ artillery accident, to the surviving gunners who got their injured and dead mates away from the gun and made safe the remaining ammunition -- despite the fact that they were themselves missing limbs or eyes in some cases. Seriously tough -- and they were just NS boys. I think a NZ Army SGT also got the medal in the same incident. There are a few others which I can't remember.
I think that the Medal of Valor is also the highest award given out so far, so MINDEF has high standards. That is a good thing.