And the mystery plant. Can anyone ID it? What can I do to get it in better shape?

I don't think you can take it off the mount once it's mounted. Even if you soak it for a day, those roots aren't all going to magically lift off. You'll end up tearing them off and killing the plant.

Thanks. Poop.

you can trim the stuff that is dead and lifeless. If you can hang them outside where they get a little morning sun. Bright shade the rest of the day. Water every day. Maxi-crop will make them happy. Creates strong roots. You can buy it over the net I think.

https://www.google.com/#q=maxicrop&tbm=shop&spd=4939986914464224492 

Powdered form would be best for you. Shipping a gallon would cost. Shop the web for the best price. That was the first one I found...

I'll see if it is available to import into Mexico. Often, even products that sites indicate CAN be shipped to Mexico in fact get stuck at Aduana (customs). I may try inquiring with Aduana.

I have a friend who is supposed to be bringing me some Dyna-Gro 9-3-6 and ProTekt, but I've never used them on orchids.

I've got a south-facing balcony, but I expect that's too strong. Given my location, I wonder if hanging in north windows might be okay.

I'll clean things up & go from there.

At your latitude the north window might work...

bottom plant looks like a stanhopea, when it blooms, we can easily identify the species.

I would soak the stanhopea and ease it off the mount and get a wire basket with coco fiber liner and filled with sphagnum moss. Stanhopea do so much better in baskets. By the size of their leaves they go through a lot of transpiration and need a lot of moisture to compensate for it. Leaving in the mount will require constant watering and not grow nearly as well. A cool thing about stanhopea is that they will bloom pointing downward from bottom of basket, so basket needs to have many openings for flower spike to push through. They are heavy feeders when in active growth and although the flowers last only a few days, a well grown plant (n a basket) can be blooming for quite a while and finally they are incredibly fragrant. I mean knock your socks off 50 feet away fragrant.... in case anyone there is allergic to plants (like I am) Pic is of a stahopea candida in basket with flower spike hanging below it, just to show how much better they do in a basket.

To remove the mount, I would soak it for an hour or so, cut any retaining string or rope, then grab all the bulbs together and gently wiggle them side to side as a unit until the roots loosen off the mount. Then the bulbs can be placed on top of the sphagnum filled basket and tied with a wire through the bottom to keep it steady until it roots into the medium, then wire can be removed as plant is established into new medium.

Thanks for the suggestions. I'll update any progress on these two.

Ben, can you explain a bit more your suggestion of "coco fiber liner" please? Do you mean I should buy one of these (pic taken from a google search)

I may have to make my own basket. I'm not seeing any for sale online within Mexico, oddly. I want to say I've seen some being sold by the side of the road, but I could be deluding myself because I cannot for the life of me remember where.

A round metal basket would be first choice, second option a square orchid basket made of hardwood, lined with coconut fiber and filled with sphagnum moss.

Here is a picture I found on google search, a basket of 8-10 inches diameter would be ideal