The Pri Migadim and Tadir

As mentioned previously, R'Chaim Brown has a post about hadlakas menorah and tadir v'sh'eino tadir.

I would just like to add 2 points to the discussion.

1) The Pri Migadim in Siman 689 writes that really Ner Shabbos should be lit before Ner Chanukah due to tadir. We don't do it like this because we are m'kabeil Shabbos when we light Ner Shabbos. He gives an eitzah of how to remove this problem of tadir by saying that you should not have the Shabbos candles set up when you light the Menorah. Then you have no shailah of tadir.

The question I have on this is it seems the Pri Migadim holds that tadir doesn't apply if it is a z'man chiyuv for two mitzvos. Rather it only applies if both mitzvos are mamash in front of you. When you light Ner Chanukah, isn't it also the z'man for lighting Ner Shabbos? What difference does it make if the Shabbos candles are not set out in front of you. It is still the z'man for lighting Shabbos candles.
Also, would it make a difference if the Shabbos candles are in one room and the Chanukah candles in a different room? L'fi the Pri Migadim would that be an issue of tadir?

2) There is a shittah (I believe that both R' Moshe and R' Ahron Kotler held this way) to light the menorah around 15-20 minutes after sh'kiah. The question is , would it be necessary to daven ma'ariv beforehand or since it is not the z'man for ma'ariv there is no issue of tadir.