Suggestion is different from check and balance. In an earlier posting I've already pointed, the President opens Parliament with an address. In that speech, the President can suggest any policy direction he deems appropriate to suggest. Of course an influence is exercised, but Parliament has to make up their own minds eventually through debating and voting. The President cannot check and balance Parliament since he cannot participate in parliamentary debating and voting. The results would then be forwarded to him to assent. He must assent. That's his job to represent assent for Singapore as whole, not his job to question or check and balance Parliament.
As for the reserves, he has a right to veto, that's all. For example, if the Government wants to spend $XX billion on converting Geylang into legalized integrated sex resort, he should veto. But if the Government wants to spend $XX billion on packages to help citizens, who in his right mind would veto? The only possibility is an anti-PAP President there for the sake of opposing PAP. He may claim that's vote buying and veto. Lose-lose for all.