She goes to church and I don't, but I believe that I take the church with me everywhere that I go. When I come together to fellowship with other believers, I consider that a form of church. Is it wrong to think that way?
First of all, the ekklesia is two or more believers gathered in Christ's name it is not an external thing that one can "take with" or "go to".
I feel like she was telling me that I need to become an active member of a church in order to have a covering.
This is very typical of those who are part of the Christian religious system. You have Jesus as your covering already so what could possibly be lacking that man can add?
Does "being covered" mean being a member of a church with a pastor in charge of my soul? I want to understand what that term means.
I believe that that is the what is implied by "covering", it is generally a religious term used to support the man-made clergy/laity system.
Is it necessary to have a mediator between myself and Christ? Is that a covering?
Is it possible? Yes. Is it necessary? Absolutely not. All though many would argue, in essence that is exactly what this type of covering is, and when observed in proper light it can be a serious stumbling block to real spiritual life.
Is it a mentor who is futher in their walk with Christ?
A true spiritual mentor would not make the demand that you belong to a religious denomination or group, they would already understand that there is one body, and it belongs to Christ and is governed by HolySpirit.
Is it possible to have a "covering" without being a member of a church?
In the terms that have been discussed in this thread I don't think so. I don't see any purpose for it outside the religious system.
Can my spiritual gifts be developed outside of a church?
Absolutley, my family and I have witnessed the spiritual gifts working many, many times and we haven't participated in any of the religious system's liturgy or functions in several years.