Deciphering Abe-Chan / Phone Calls / Ne?

I’m sure many of you have seen the video of Abe-Chan speaking with his owner about answering the phone:

Now looking at the snippet below (as I heard it), it sounds like Abe-Chan’s owner has inserted ね at unusual points in the sentence. Is this a colloquial thing (or something I’m missing?)

ちょっと早い…
ちゃんと**ね**電話が**ね**掛かって来たらもしもしするんだよ

As for the full clip, I’m able to comprehend most of it, but still missing a few pieces:

* Is she telling Abe-Chan 「早い」 because the phone hasn’t rung yet, or more of a “don’t rush” because he answered improperly?
* I haven’t heard 「ですけど」used to trail off at the end of a sentence before, but apparently this is common? Is it standard for this type of phone greeting, or just used in general conversation?
* 「掛かって来る」is a new phrase for me. Is this often used for receiving phone calls?「掛かる」seems to have such a ridiculous number of usages.

Thanks to anyone who can help clarify; I take Abe-Chan very seriously!