せい/ あったとします/ しゃがない

I came across a few terms I wasn't sure on, and I'd like to confirm their meanings and usage.

1. 先生の話し方が面白がったせいか、彼は話に聞き入って しまう。
What is the meaning of せい here? Is it similar to 風(ふう)?

2. 私達の行き先に壁があったとします。
Does "があったとします" here indicate a hypothetical situation?

3. Is しゃがない a dialectal variety of 仕方がない?

4. 日本は皆さん、この基調講演にお越しいただいて、誠に ありがとうございます。
Is there a difference between using 日本は皆さん and 日本の皆さん here? Is it just a point of formality? Or is this speaker considered a representative speaker of Japan, hence the は?

Thanks!

1. That's not 面白かった? No, it's not like ふう. It's more like the せい of お前のせいだ.

2. Yes.

3. It's not しょうがない? I'm not familiar with しゃがない.

4. I think you reversed the order there. It should be 本日, not 日本.

1)
せい indicates the reason/cause.

2)
Right.

3)
Isn't it しゃーない or しゃあない? If so, it's from しょう（＝仕様）がない. (しゃーがない / しゃあがない is also possible only in some dialects.)

4)
It doesn't make sense. It would be a typo of 日本の皆さん.


EDIT:
Ah, indeed it could be 本日は. I initially thought it might be 今日は[こんにちは].

Sorry Glenn, yea it's 面白かった. Slip of the tongue for me. I always think of かった is closer in sound to がった especially when it's said fast. My teacher has pointed out to me it's wrong....but I still think so.Thanks to the both of you for the replies.

3. The exact sentence is worded "あまりみっともなくはしゃがないでくれるかしら。" She says it to a guy who goes "うわー！すげぇー！".

It could be that I partitioned wrong? Or.......is はしゃがない actually the present-negative of 燥ぐ? That might make more sense......Sorry for the mistake. Wasn't aware of the word until I looked it up just now. Assumed incorrectly in this case.


4. Wow.......it must have been a very long day for me. 本日は makes much more sense. I can't believe I got the two mixed up. Sorry about that

Thanks again, both of you! I really appreciate it.