I am meeting the elderly adoptive mother of a good friend for Christmas, this lady is Japaneses by birth how do I greet her verbally and what type gift is appropriate? Any other proper customs I should know about?
Hmmm First of all, you may introduce yourself as it will be the fist time you meet her.
So while bowing " Hajimemashite, (name) desu. Yoroshiku onegai itashimasu" I use to bow twice, one time when saying the first sentece, and a second time at the end of the second sentence.
Then for the gift, I don't know but a good bottle of wine, tasty chocolate, or flowers are quite good I think. It depends on the age of the lady, and also the purpose of the gilft. A book, is also a good idea. Then when you give to the Lady the present, you may say, if you want to seem very polite " Tsumaranai mono desu ga..." presenting the gift with BOTH hands.
When leaving, (if it is the house of the lady), " kyo ha iroiro o sewa ni narimashite, makoto ni arigatou gozaimasu" while bowing.
I'm a Japanese, and I rarely see Japanese people shaking hands when meeting for the first time or while saying goodbye. I shook hands all the time when I was in the States, but I never do that here, at work or personally.
I think a deep bow when you introduce yourself would look nice and cute, especially if you're non-Japanese. But despite all the complicated phrases that people gave here, my general advice would be: as long as you know some real basic Japanese greetings, just be polite and show you're happy to see her, and that's really enough...