You ask: As the bonds (on the secondary market) near maturity, does the the yield curve change to reflect that?
And my answer is: NO the yield curve does not change. Just the discount on the bond changes.
http://en.wikipedia.org/wiki/Bond_valuation
You ask: If the US government issued a new batch of 10 year treasury bonds - would they need to be issued at a coupon rate close to the 10 year bond yield rate, to attract investors?
And my answer is: In principle YES.
You ask: What is the significance of the yield curve?
And my answer is: the long term rates are equivalent to short term rates plus a risk premium for having to hold the bonds for a longer period, a premium that does not need to be positive. And the yield curve shows that.
You see, a long term bond can be viewed as a short term bond whose interest is being continuously compounded until the end of the long term period. As short term interest rates may change during the period of the long term bond, investors ask for a premium to cover themselves against that possibility.