While some information will be available, the meeting minutes, etc will not be as they are intenal records.
You really have not identified the issues you are concerned with here. But you can determine pretty easilly if they are duly qualified as a non-stock entity with your state and have received a 501(c) tax exempt status as a church. If so, they really have few formalities they need to adhere to.
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While I agree that board minutes are not typically subject to public disclosure, I see you are in Texas. If you are a member, you may request copies by making a written request stating a proper purpose. You also ask what is filed annually with the IRS. Unlike most types of charitable organizations which file Form 990, 990-EZ, or 990-n, churches have no annual filing requirement unless they have voluntarily taken that on. The exception to this is form 990-T which reports unrelated business taxable income -- that is income from a trade or business regularly carried on that is unrelated to the exempt purposes of the organization. If the restaurant and wedding hall create UBTI, the church would file a 990-T with the IRS. However, many churches consider activities like coffee shops in the church and wedding halls to be related to their exempt purposes.
I would add to Mr. Moore's response that some religious organization voluntarily file the 990. If so the church in question has you can easily get a copy at guidestar.org.