1. I have heard of rinsing the tea to get rid of caffiene but I like caffiene so I don't do it regularly. When I have done it I usually just kind of rinse tea through my infuser [basket style] pouring a cup's worth of water very slowly and dunking it in the cup a few times. I don't know how I would do it with an ingenuitea :/ and I don't know how much caffiene it actually shaves off.
2. I don't know...but I'm sure not ALL the healthy properties go away and I bet rinsed regular tea is still a lot better for you than water or other beverage alternatives. I'm sure it doesn't magically become bad for you or anything
3. I am a HUGE cheapass...I will use the same tea all day sometimes...but it depends on the tea and how long I brew it. Of course the 4pm cup is WAY lighter than the 10am cup but it's still better than plain water or soda IMHO. Actually...on some teas I kinda like the second cup better [hello gennimacha! over here!] It just does not work at ALL with some teas, esp flavored teas, where the subsequent infusions taste like crap...but hey experiment and find out what you like best! I find though that I usually steep that second cup the same amount, not more. I've heard people say add a minute for each reuse but I think it just overbrews it. I also have heard don't let your tea dry. If you used tea leaves yesterday morning and they are dried out don't brew it again. I dunno why exactly....but to test it I left tea from the evening out and brewed the dry tea again and yeah...it didn't taste good...but I know a second infusion would've tasted okay normally.