Probably not, probably not, and more or less 
There's nothing preventing early-time acceleration (inflation) and late-time acceleration (dark energy) from being caused by the same thing, but we have no reason to suspect they're related, either. Most viable theories of both are not related. As for late-time acceleration, dark energy is the name we give to whatever it is that's causing it, and the cosmological constant is a particular candidate for that (and the leading candidate right now). It's a specific kind of dark energy where the density is constant over all space and time, never evolving. Most other models of dark energy show some deviation from this over time.
There's nothing preventing early-time acceleration (inflation) and late-time acceleration (dark energy) from being caused by the same thing, but we have no reason to suspect they're related, either. Most viable theories of both are not related. As for late-time acceleration, dark energy is the name we give to whatever it is that's causing it, and the cosmological constant is a particular candidate for that (and the leading candidate right now). It's a specific kind of dark energy where the density is constant over all space and time, never evolving. Most other models of dark energy show some deviation from this over time.
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