Muslims are allowed to kill animals for eating purpose but it is forbidden to kill them in order to have fun. Also it is allowed to kill spiders, snakes or other animals who affect our life, but we must not destroy life more than it is necessary.
Allah swt, the Almighty, created each being in this world for a specific reason and each being does something useful which we might have no knowledge about. Allah swt gave us power over animals. They help us in different ways and make our life easier. We must be grateful to Allah swt for this also by having a good behavior concerning animals.
The Prophet saws said that it is a reward for every good thing we do to a being. A Muslim must be helpful always, have good deeds and avoid bad actions, violence. If we see people who treat bad animals then we must stop them from doing it.
Muslims are allowed to have cats inside home. If we take care of cats then we will get big reward in the Hereafter life. Many companions will enter Paradise as reward for giving food to hungry cats. The Prophet saws gave to his companion Abdur-Rahman the name of Abu Hurairah meaning ” father of cats ” because of his love for cats ( he used to have a cat with him always, wherever he was ).