About long enough to go from the headset jack to about the same place on the other side. The dead headset I cut this off of had an angle plug on it. You can route it ether way or just let it dangle.

I suppose one could work out the dimensions for a 1/4 wave at the middle of the FM band, but what I have is certainly shorter than that and seems to work well enough for me.

The blue tack is just a small ball of the stuff crushed around the wire and stuck to the case, I'd have to look but I have 3, I think, of them spaced along the wire. Easy enough to remove and reposition as necessary. I did clean the wire with a quick swipe of alcohol, although I am not sure that was strictly necessary.

Also, I was careful to make sure the cut was clean, nothing shorted together in the process. Might be smart to put a dab of super glue on the end of that to keep it from fraying and shorting though. Or perhaps even a blob of hot glue, just so whatever you use isn't conductive (probably not likely, but one never knows ...

HTH