Fund space. I agree with Juliekcmo that the room should be set up to be the most functional and enjoyable for you for the 50 weeks a year that you occupy the space. I would put the couch in the alcove, and put either a sofa table behind it or hang a shelf on the wall behind it with brackets. That is the place for a lamp, a clock/radio/mp3 player, a place for someone to put a glass of water and a book at night. That also means that the window isn’t blocked so the room gets the benefit of max light all the time. Fan should move out into the room - do a cute chandy in the alcove, something fun and whimsical. The small chest that you have ready to paint seems like it would be the perfect companion piece for you to use for spreading out your files as you work. I think it would fit with the bookcase on the end wall to the left of the entry door to the room, based on the measurements you gave. Bookcase in the corner so that you can have clearance for the chest drawers once the armoire is on the other wall nearby. Then the armoire would go on the long wall, toward the bookcase and chest, to create the feel of an office area. It should still allow the computer to be visible for someone on the couch. To the left of the armoire, I would place the cute wood table you love, with a lamp. The tall mirror might work above this, to bounce some light around and feel anchored. Then angled in front of the stationary part of the french doors, your desk chair can be placed when you are not working. To the left of that, the little set of drawers, which seems perfect for CD storage, so that you can get them off the top of the armoire. You will then have a seating area for someone visiting if they don’t want to sit on the sleeper couch,(especially if it is opened), or you can sit and talk to your son in there while he is visiting. I would put the ottoman on the short wall to the left of the french doors, to get it out of the way when the bed is unmade or it isn’t being used with the couch. I would frame a grouping of the Audubon pix and place them on the wall by the closet. You could do a few more stacked over the ottoman. As for color, I know you said white, but I would think about a color that makes you happy to use in the workspace. I love the purple accent wall in the alcove, and if you still like it, that could be your other color throughout the space. Your pieces to be painted could be done in another (or the same) shade of purple. I could easily see green walls in there, something restful but deep enough to work with the large black pieces. I would paint the bookcase the the chest the same color if they are going to be next to one another, for a more cohesive feel. Consider something textural for the drapery and french doors, perhaps a textured linen or hopsack.

Instead of a Murphy bed, you could do a Murphy DESK aka wall desk. Bed and chest (or nightstand) should go on the wall where desk is presently located. Murphy desk would go on opposite wall. It means you can't have papers lying around as table top would have to be pulled up when expecting guests.

I do like it, and if you and mil like it that's the most important thing. I found this photo that really shows how good this colour green looks with natural, mid-tone wood. I don't love everything about it but see how the wood and green just compliment each other so nicely? The silver is definitely nice too, and if you go with it I would do black or blonde wood floors with black and white rugs. The rugs could be geometric design, stripes, zebra, whatever. Then use black for the bookshelves, silvery grey for upholstery. It would be a very glamourous room so I'm not sure it would be conducive to your mil's intended purpose (devotion, prayer, and entertaining guests).

I was thinking of an aqua blue with the lime-ish green and silver you have already determined you will use. Would be a little calming with the brighter elements. You can sometimes find smaller, inexpensive upholstered chairs all over the place....overstock, Pier 1, Wayfair, etc. I would also make sure you used those colors in the rug and maybe a pillow or other decorative pieces.