Tai Chi is a form of kung-fu, a fighting art developed in China over the last thousand years. You may be interested in History for more information.
Yes, but there is a caveat. Today Taijiquan is rarely taught as a martial art and is usually practiced only for health. If you are interested in learning “Tai Chi” as a martial art, you can still do it but you will have to find a teacher who is capable of using Tai Chi as a martial art in the first place. Most instructors cannot do this.
A quick way to tell if a Tai Chi school will help you learn to fight is whether or not they teach co-operative push hands. If the school does not teach co-operative push hands, or does not teach push hands at all, it is likely to be a complete waste of your time. Generally you want a school which is not afraid to show it's stuff – there are hundreds of good Tai Chi schools in the world, it's not a “secret” anymore. Humble teachers are famous teachers!
Qi (various spellings) is the internal energy of the human body. However, you have to be careful because saying 'internal energy' has just traded one term for another; now you need to know what internal energy is. You are probably looking for the Chi FAQ.
This means, what is the role of supplementary exercises like standing meditation and silk reeling exercises. Chen Zheng-lei explains,
In the old days, children would begin by learning forms right away, in the traditional manner of learning sequence, corrections to movement, and then developing internal energy. Now, things are more sophisticated; children begin training with flexibility exercises and “chan si gong” [exercises for training silk-reeling energy] but do not begin the forms for a while.http://taiji-bg.com/articles/taijiquan/t27.htm
Traditionally, everyone begins with Lao jia, Yi lu [old frame, first routine] at first. From there, they learn the single-edge sword [broadsword]. After training in Yi lu for two years, the body is relaxed and the student begins learning pushing hands and Er lu [the second barehanded routine of Chen Style].“