I'm under the impression that if I Wildshape as a Druid into an animal that I use the restrictions listed for the Beast Shape spells. However I am confused about stats and hit points. I think that my hit points stay the same as my druid form but could be modified if the Beast Shape spell says my con score changes. I'm also not sure but I assume that I keep my stats the same as my druid form unless the Beast Shape spell says something changes.
Your assumptions are correct, but you probably want to review the polymorph rules on general principles. Your stats stay the same unless the spell says otherwise or it changes your size.
You are correct about HP; they stay the same unless your Con changes, in which case they go up when you shift and then back down the same amount when you revert; in theory this could mean that reversion kills you.
Also what happens when your animal former loses all of the hit points? Do you die or revert back to druid for with the same hit points you started with?
If your HP reach negative Con, you're dead, regardless of what form you're in.