Let’s see what we can agree upon.
The Church is the union of all baptised believers.
Yes
The Church is an institution founded by Christ to assist all men learn about the Good News.
The church does not exist independent of believers. It is not an “institution” with a separate existence.
The Church is one in doctrine
I’d have several caveats with this. Paul said it was OK for there to be differences, even in seemingly faith-based issues such as what is appropriate to eat or drink, or what days are held holy, etc. If you simply mean, “one in doctrine” on the basics, or salvation issues, then I’d ask you to define the basics.
The Church is Apostolic in nature and history
This is vague enough to mean just about anything.
The Church is holy: founded by Christ and Guided by the Holy Spirit.
Yes
The Church is catholic: universal for all men in all times.
Depends on what you mean here. It has never reached all men in all times. It took 1500 years just to reach the New World. I’d revise this to say that its
purpose is to become catholic and reach all men (The Great Commission).
I’d actually add a few statements from scripture, in addition to defining the word as Sambos has done, as well as providing some prophecies regarding the church.
The church is the Bride of Christ.
The church is the Body of Christ.
Christ is the head of the body.
Depending on how you interpret them, some of your statements could be considered mutually exclusive. E.g., since I’m validly baptized, I’m a part of the church based on your first criteria, but since I don’t fit in with other doctrines of Catholics, I am not a part of the church. So, my question would be, are they all required?