He's a heavy smoker as far as I'm aware. Smoking might not have an immediate effect if you hydrate yourself and your technique is impeccable but in the long term with the number of shows he used to do, goodbye voice.

I have another question about Geoff. He is claimed to be a baritone, by Thomas Appell for example. He trained with Maestro David Kyle (http://www.myspace.com/maestrodavidkyle). Does anyone know what kind of singer he was before his training: range, style, technique?

I would imagine a baritone. He has been a baritone all through out his career.

What's his technique like?

It was great and I believe it still is to a degree, I say a degree because I think he still has good technique just doesn't take care of his voice. I've seen a number of rumors that he smokes just before going on stage. I don't follow Queensryche anymore, Geoff's voice is just disappointing and their songs are terrible anymore.

Old Geoff:
http://www.youtube.com/watch?v=Jfn4njkZmAc

New Geoff:
http://www.youtube.com/watch?v=rcVDCeockZ8&feature=related

Geoff Tate is the one singer responsible for definitively inspiring me to sing.

There's an interview in youtube where he talks about how he took advice from Meatloaf about letting your voice be your voice. I think that's when he misinterpreted things and stopped maintaining his voice.
Ever since I've followed what has happened to him and he has quit smoking, although his teeth are still yellow. His voice has recovered partially.

There's something else that influences that. His approach. Since Rage for Order he started a different approach whereas he wouldn't concentrate so much in singing technique and as he called it : "showing off" as he did on interpreting the song from feeling. He said so in an interview celebrating the 20 years of Queensryche posted in their site(you can follow a link they have on Facebook). I think the best example of that new approach is Silent Lucidity, it took him 5 takes a dinner and one more take to get the song. He did the last take in one settle, no interruptions.

Then if you move up to the Promised Land album you can hear he's actually screaming in Someone Else's last verses when he sings:
"There so much more I can be"--forced/throaty scream on be.
You also have to remember he played the Trumpet on his high school band for two years in a row before ever taking singing lessons. So that partially explains why it only took him 8 lessons to get that good. He already knew good support.

Geoff's singing reminds me of how girls talk. Girls are so expressive with their voice, it's like they're dancing with their voices, ha. And Geoff sings that way too... always all over the place. Like a drama queen :)

Wrong. It also depends on the day. I betcha that if he took care of his voice he'll be golden.

listen:

http://www.youtube.com/watch?v=kyB3OFduIz4&feature=grec_index