Don't we actually already have evidence of other cases of the NSA adding backdoors to widely used systems, exploitable by anyone aware of them? Isn't that what the elliptic curve backdoor was? http://www.wired.com/2013/09/nsa-backdoor/all/
Apparently your assumption is quite not safe to assume.
I guess the NSA either figures nobody else will notice the backdoor, or just doesn't care. I guess only they know their motivations.
It doesn't allow just anyone to break it - merely knowing the backdoor is there isn't enough.
I don't see why people think that NSA is simultaneously genius-level forces of the Illumanti architecting events that will culminate years later, and yet would make the rookie level mistake of introducing a backdoor that is protected only by obscurity.
They know other security services understand how to decompile code (or read the original source).
More importantly, they know that critical government services they can't predict will end up possibly running things like their broken version of OpenSSL. There's a FIPS standard, of course, but note that the Heartbleed page made quite clear that FIPS is vulnerable too.
If possible, yes. However, if they were indeed responsible for this, they'd probably have a couple honeypots to detect exploitation by third parties. If they considered the third party harmless, they could decide whether the vulnerability should be "independently discovered" or not.
Planting a complicated exploit would be harder and increase the risk it could be traced back to them.