Do you spell out Thm., Prop., Eq., Ch. in mathematical papers? Just as the title says: do you spell out Thm., Prop., Eq., Ch. and comparable abbreviations in a mathematical paper?

I suppose that, if in doubt, it is always best to stay consistent (in whatever way) throughout ones writing for the least. Do journals have (different) policies on this, or is there a prefered style when in doubt?
It is a matter of style. I would say yes, expand them. In my opinion, authors tend to over-abbreviate making documents harder to read. For instance, I can't work out what you mean by Ch. (Conjechure?)