Does the US still have the neutron bomb in its nuclear arsenal? I’m just curious.
No, but Australia does.
Yup.
Olivia Neutron-Bomb. 
Don’t know, but I found it amusing that in one UK newspaper (the Guardian?) they described the Neutron bomb as “capable of destroying biological weapons without damaging surrounding structures”…
Well, yeah it’s accurate, but way to miss the point guys… 
Interesting way to put it.
That is inaccurate- Neutron bombs do have a good-sized explosion, and they will damage surrounding structures. The main difference between a neutron bomb and a normal nuke is a slightly smaller blast for a lot more radiation.
Not in any substantial numbers, if at all. As this 1991 article describes, the neutron bomb was deployed in the 80s mainly in the form of Lance missiles. More specifically, it became the W-70 warhead used to arm them. However, by 1999, when he testified before the Senate Armed Services Committee, William Cohen was able to say:
Furthermore, this FAS-endorsed description of the current US stockpile doesn’t include anything resembling a neutron bomb. The strategic circumstances had, of course, shifted since 1991.
The US does however, presumably, retain the capability of manufacturing such warheads should their possession be deemed advantageous.