Can I use a sieve to increase frying oil life?
Your pasta sieve will not be fine enough and it will not prevent what you think it will. The particulates in the oil that burn are burning because your oil it hot enough to burn them. Keeping them suspended above the bottom won't prevent the burning. They will still be submerged in hot oil.

When your oil starts to get older simply run it through a very fine mesh or filter (I use coffee filters) to strain the sediment.