1. Which vegetables do you ferment?
I ferment cabbage and other
brassica-family vegetables. My favorites are regular sauerkraut and kimchi with napa cabbage or Korean radish. I make fermented beets and other greens a few times a year.
2. What is the process of fermenting the vegetables? (any link for detailed explanation?)
For Korean-style fermentation, I like this one:
http://www.maangchi.com/recipe/easy-kimchi. My kimchi does not use oysters, and very little chili flakes, but I do make the "porridge" paste that is shown here. I use that paste for all fermented vegetables in the Korean style.
For traditional sauerkraut, here is a good site:
http://www.wildfermentation.com/resources.php?page=sauerkraut. I have Sandor Ellix Katz's book
Wild Fermentation.
I have been fermenting for so many years, and I keep a simple style, using glass jars no larger than one or two liters. When I was growing up, we had to process so much at the end of the summer, it was weeks' work and very tiring. Now, I buy a cabbage or other vegetables any time of year, chop it up, get it into a jar, and I'm done in 20 minutes.