1. Thunder Hooves lets you move through enemy squares, which you normally couldn't. This still provokes OAs.
2. Thunder Hooves grants you extra damage when you've moved through an enemy. Pressing Strike lets you move through an enemy. I think they'd have to interact. In this case, you could use Pressing Strike to avoid the OAs via its free shift.
It doesn't state how, so yes, should work by RAW. Intent is a different beast though and we can argue about that until the sun explodes . By RAW, it works with pressing strike.
And if you do not use pressing strike, yes, you grant an OA, since that is what you do if you enter the square of an non-helpless enemy and that the power does not state that you do not provoke