The hardest part about this topic is defining the term universe because there can be an infinite number of different interpretations of the word depending on who you ask and the frame of reference in which they are asked. Many different people and animals will see the universe in different ways and in different circumstances. A person will perceive the universe a different way than a dog or cat. A person in love will perceive the universe in a different way than a person who has been saddened by a loss. Even the physical universe can be perceived differently by different people. A primitive person who knows nothing of the outside world may believe that there is nothing more as compared to a scientist who studies astronomy. If all these perceptions and beliefs contribute to the size of universe then the universe should indeed be considered infinite.
The size of the physical universe may or may not finite but there is no way prove it in either case unless you are the Creator. Until God reveals the answer to this question to us we have to rely on the technology we have at our disposal to try and speculate on the size of the universe. Based on the observations made by the Hubble telescope the visible universe is somewhere around 50 billion light years in diameter and is expanding outward. How far and how long this outward expansion will continue nobody knows and probably will never know. One can not assume that the outer edge of the expansion is the limit of the universe because it must be expanding across something that must be part of a larger universe.
The idea that an infinite universe would contain infinite stars is ill-conceived for the simple fact that even an infinite number of stars would be producing a finite amount of light that travels at a finite velocity. The velocity of light is 300,000 km per second but is subject to what is known as an inverse square law where the further away an object is from the light source the less light the object actually receives. If a light source is an infinite distance away then the object would receive no light from it; it’s actually a lot less than that but the concept is still valid.
One cannot logically conclude that the universe is finite because some evidence suggests that it is. Neither can one assume that it is infinite based on the technology that we use to study it. The simple fact of the matter is that we don’t know and we probably will never know without some help from above.