Can a Rinnegan user use Mangekyou abilities?
To put it bluntly, no, the rinnegan cannot use mangekyou abilities. As you can watch in the anime, Madara can switch between Rinnegan and Sharingan because he awakened both.
Nagato only had the Rinnegan.

Basically, the Rinnegan isn't an upgraded Sharingan, it's what comes next, but it's a completely different eye.