Stereo & surround mixes in same project?

Nothing.
I use the brickwall limiter from the Dynamics Secion.



When using a send to route from a 5.1 Out to a Stereo out, how does it get downmixed?

Automatically. You don’t have to worry about anything.

Or is this routing not for downmixing, just for both kinds of projects (Stereo or 5.1) and then just choose which outs to export?

You “master” is always the highest track count. These channels, you downmix to lower channels.
We export all the outputs in one go with Channel Batch Export

How do you do up and downmixes from this? Lets say, a mix original mixed in 2.0 has to get upmixed for international use. Different session or also done in this setup?

Upmixing is an entirely different beast. A project that is mixed in 2.0 needs to be Re-Mixed for 5.1. Start from -nearly- scratch.
Or use an Upmixer like Halo. Which is normally only used for upmixing stereo music within a 5.1 project.

HTH
Fredo