I sense that you will probably get different and varied answers to this question. Different teachers will have different levels of comfort in the issues you identify. I think it's pretty courageous of you to ask the basic questions about the competencies of an English teacher as it demands reflection and, frankly, is something that all teachers should be open in engaging.
I don't see teachers of English as any different than any other learner or reader. English teachers have their own strengths and weaknesses in reading literature. Some might have a strength in one particular type of literature, while another field of literature might present a weakness or challenge of sorts. For example, some English teachers are more well versed in Shakespeare than others, while others are more skilled in drama than others. I don't think that all English teachers are monolithic to be perfect in every engagement in literature. There are areas of weakness in every reader. The trick is to understand where these weaknesses are and make them stronger, enabling the lifelong learner element to be seen. In the end, teachers who are able to admit their own weaknesses in reading literature are more likely to connect with students. The idea of a teacher's efficacy, how much they are able to impact a student's learning, rests in their ability to recognize that they, too, are learners. In embracing this approach, a barrier between teacher and student is reduced. Imagine the power in a teacher being able to tell a student, "I struggle with ________, too. This is how I compensate for it" or "Yeah, that gives me trouble, also. Why don't you try _________ because it worked for me." Instant connections are made and students recognize the value of istruction because someone else who can be seen as effective in the craft of literature is in the same position as they are.
I think that it is safe to say that English teachers possess some natural comfort with reading. I don't think that any English teacher is going to be particularly effective if they stand in front of the class and says, "I don't like reading this book or any book, so let's watch the movie instead." On some level, English teachers do have a natural propensity that enables them to gravitate towards reading. However, this is not something that means students cannot embrace their zeal and appropriate it themselves. It is this point that makes for the most effective English teachers. The best of English teachers are able to relate to their students, recognizing their own weaknesses as learners of literature so that students can be more effective in their interaction with literature.