Does the biosphere have infinite resources and are they infinitely renewable?
No, it is not infinite.

The sun has not an infinite mass neither does the earth. So energy is not infinite. But we probably don't really care about that as it applies at a scale we're not really concerned with. What is important at our scale is the rate at which is the rate at which the biomass we're destroying (eating, building houses with) is produced. The rate at which we consume this biomass has to not overpass the rate at which this biomass is produced. Than, practically speaking, biomass will be produced infinitely. Of course, ecosystem stability is not that easy but it is not within the scope of the post to talk about that.