Hello! Nice render. The orange specs are called “fireflies” and they have an easy fix especially because you said that you have an HDRI. What you can do is turn multiple importance on in the world settings and increase your sample size in the render panel.
You can also check out this article: https://www.blenderguru.com/articles/7-ways-get-rid-fireflies for more tips as to how to remove them. In that article it shows you how to use a setting called “filter glossy” and I suggest that you use that in your render as well as it seems the surfaces are pretty reflective.
I’m not sure about the black spots, it might be something to do with your UV map so I’d suggest googling some solutions to that.
In order to make the background transparent in Blender 2.8 and 2.7 go to the render panel and open up the film settings. You’ll find transparency there.