2 questions about the 7 and the 9 rings

All rings of power, save the one, were forged with the intent that they should help that wielder govern their race and realm. So there was little difference between the 7 and 9. The 7 and 9 rings were intended for dwarves and men, yes. Sauron had a hand in the forging of the great rings and touched all but the 3. (which is why the three are not corrupted.) All of the 7 were lost over time, and the nine, as we know, turned the kings that bore them into ringwraiths.
***A.B.B.A.***