Battery etc

Is 'the battery etc' plural?

etc. hasn't been Anglicised in use so as to ignore other features of it's origin, so we generally wouldn't have: So there isn't much of an argument to be made for treating it any differently to its expanded form. Therefore "the battery etc." is plural.

What does the battery and other items are included mean?

The battery, etc., is included. I would consider this an improper use of the abbreviation etc. Et cetera, and its abbreviation, means "and other things of the same kind," and it is not at all clear what these other things are in your sentence. I would reword your sentence, "The battery and other items are included."

Is battery a valid construction?

Putting aside quibbles over whether battery, etc. is in fact a valid construction (I have no problem with it), the correct verb form is plural are. It's plural because the subject includes at least two things - the battery, and at least one other thing which is "similar" to the battery in this context (since etc. means and other similar things ).