Okay, lots of good stuff in this post...First thing I think needs to be mentioned though is that most teas, especially types of Green Teas, contain an enormous amount of caffeine, which can kill your bird! So I don't suggest giving your bird ANY tea that has caffeine in it...They do make caffeine-free teas, but I don't know about Green Teas that are caffeine-free, as by definition Green Teas contain caffeine. So you really need to watch this...
As far as buying tea leaves and brewing them, Yes, you can just walk into most grocery stores and buy loose tea leaves. A lot of grocery stores that have "Organic" or "Natural" Health sections, such as Wegmans, Whole Foods, Harris-Teeter, etc., actually have "Tea Sections" (Wegmans has the largest and best Tea Department I've ever seen, it's huge), and they sell both boxed teas that are in tea-bags, as well as loose-leaf teas that you can buy by the pound, and that you dispense, measure out/weigh, and put into individual bags and then print a sticker out for, just like you do when you buy loose coffee-beans or loose ground-coffee.
As far as brewing loose-leaf tea, you have to buy a "tea infuser". You can buy either a teapot that has a built-in infuser just inside the lid (I have one of these, I love it, the infuser is removable to make for easy disposable of used tea leaves), or you can buy a separate infuser. The infusers are basically little baskets or round balls that are made of mesh, like a strainer, that you open up, fill with the loose tea leaves, then close put back together. The separate infusers usually have a chain attached to them that you can attach to the handle of a regular tea pot or you can just hold, and you boil water in your tea pot, and then you drop the infuser filled with tea leaves into the boiling water, allow the tea to brew, then you just remove the infuser, dump it out and wash it, and you have tea. The teapots that have an infuser inside of them are easiest, you just take the lid off the tea pot, fill it with water, put the infuser basket inside the the tea pot, and boil the tea pot. Easy.
As far as Teas that promote weight-loss, most all of them simply contain stimulants, such as caffeine, ginseng, and green tea itself is a stimulant...The best teas for weight-loss are the ones that contain Yerba-Mate, as it is a natural stimulant that is right on-par with Ephedra. They make all kinds of tea that contain Yerba-Mate, both in bags and loose, usually they are black or green teas, and there is actually a brand of Green Tea that comes in boxes of tea bags called "Yerba Mate" Green Tea. It's pretty good, but it's potent, like drinking some Claratin or Sudaphed that contains Ephedra. It works though, but if you have any heart or high blood-pressure issues then be careful with it.