The English word "church" is a translation of Greek "ekklesia", which means gathering, assembly. Which would be kinda odd unless many people were being gathered or asembled.
Belief in Jesus Christ is an individual matter
At some level yes, but never forget that those who have a *relationship* with Christ are connected not only to Him but also to each other.
Believers are gathered, assembled, in Jesus Christ right now, who is the living church. Churches on earth are physical churches, Jesus Christ is the true living spiritual church. He will gather the members physically when He comes back.