I bought a pretty big container of vanilla almond milk. I would like to add some honey to it, and shake the container. After I use it, I'll store it back in the refrigerator. Will this be ok, or is it bad to mix honey and almond milk and refrigerate them?
The reason honey shouldn't be kept in the fridge is that it crystallises easily at low temperatures (even that's just a change in texture, not a spoilage problem). Once mixed with plenty of water so the sugars are dissolved, that won't be an issue.
I would expect the addition of what's essentially sugar to have no negative effect on the keeping properties of a water-based mixture, but this is where we can't be certain. If you stick to the use by date, and in particular the "once open use within..." instructions (which are probably to use within a few days) you should be fine. There's a slim chance you might reduce the margin built in to these dates, but that's probably all. What's more important is to avoid getting it warm for a long time while mixing