If the recorder's nice, and you want to be on the safe side, you could find a local woodwind repair shop and ask them to reattach it for you. It shouldn't be a huge job for them.
On stopping notes (and this might be rubbish, I might be pontificating wildly from a position of ignorance here):
(1) This really only applies to the last note of a phrase; the rest are normal articulation.
(2) Yes, you can stop notes with your tongue to avoid the drop-off, fade-into-flatness effect that OaG described. But it's not a flat-out aggressive tonguing, it's enough just to gently touch the tip of your tongue to the top of your mouth, hard palette bit behind the top teeth. You can do this quite gently.
(3) It's a bit like doing a hill start in a car, backwards. In a hill start you are just taking the brake off at precisely the moment where the engine/clutch is supplying enough oomph to make the car go forwards. It's a matter of coordination. In stopping a note on the recorder you're ceasing to blow down it at the same time as you're putting the brakes on with your tongue, and as you get better at it, the more you do it, the better your coordination will become, until you're half stopping-blowing, and half tonguing. That way you will neither have the drop-off-flatness that would happen if the lungs did all the work, nor the abrupt stop that you'd get if you try to keep breathing as you apply tongue-stopping.
(4) Older books, in any case, tend to discuss quite strong articulations for normal notes, e.g. T-K consonants, which are maybe more appropriate on instruments with a stronger wind-stream. On a recorder, D or G are good consonants for general-purpose articulation (and if you're using them, gently, in normal articulation, it will seem more natural to use them in the special articulation of the end of a long note). Even gentler articulations are often useful on a recorder; one of my favourites is did'ling successive notes.
Yup, the ideal lung-build for recorder is to be able to generate about 3 cubic yards of air, but at a pressure that won't even extinguish a candle. An oboist needs to generate about 4 cubic cm of air, but can blow up car-tyres by mouth...