Are there infinite questions?
If your question is about the number of question that it is possible to ask in this universe, given that there is a finite number of particles with a finite number of states and a finite number of possible transitions, you cannot have an infinite number of questions in a finite interval of time.
Is there an infinite thing?
There are finite sets and infinite sets. Sets that have more elements than any natural number are infinite. The set of natural numbers is infinite. Two sets have the same cardinality if we can pair up everything from one set in the other with nothing left over.
Is it possible that knowledge is infinite?
Absolutely, knowledge is infinite. There is no way one will ever know everything unless that individual dedicates every moment of his life to understanding everything, which is still impossible. For instance, every single community in the world has completely different dynamics with different people.
Is everything that is known about everything finite?
If we take knowledge to be knowledge of something, it depends if reality is finite or not. If reality is finite, then everything that could be known about everything could in principle be finite though very, very large. There are several ways in which reality would need to be limited to be finite:
Is there such a thing as an infinite quantity?
One area in physics where infinities are sometimes predicted to arise is aerodynamics or fluid mechanics. For example, you might have a wave becoming very, very steep and non-linear and then forming a shock. In the equations that describe the shock wave formation some quantities may become infinite.
Is it possible that reality is infinite?
Yes it is. Reality is infinite. Even your bedroom can be divided infinite times until you get to the smallest particle possible. And you could still divide that particle by half and so forth. Human apprehensions of reality through the senses can also be infinite.