1.  Is the gai in gaiatsu the same root as in gaijin?

Exactly.

2.  atsu means pressure? Is that (厚)? If so, this is interesting to me: when you're playing go, it is a good thing to develop atsumi (厚味), which is a quality of a local position which radiates influence and can be used to attack nearby isolated enemy stones.

I am not that familiar with go, nor the term 厚味, which actually doesn't even come up on one popular translation site I use --

    http://www.alc.co.jp/

--

although it does come up on this other site:

    http://www.csse.monash.edu.au/~jwb/cgi-bin/wwwjdic.cgi?1C

(This indicates to me that the term may be somewhat archaic, but I'm not sure.)

You may know that Japanese has TONS of homophones, which makes it very easy for confusion to arise -- and to pun -- in Japanese.

For example, on this page --

    http://www.csse.monash.edu.au/~jwb/cgi-bin/wwwjdic.cgi?1B

-- try typing in "atsu" in the text box and hit "Select Kanji", and you'll see eighteen different characters come up... although for some reason 厚 is not coming up...  f(^_^;)

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