Find an experienced welding shop and have the arm TIG welded back on. Remove the wires before welding and pull them back in afterwards. Trying to splice with tubing and epoxy will result in a weak assembly that is likely to break again.

(1) Remove the white trim. (2) Repair the drywall (holes, etc.) (3) Get the stairs stained. (4) If the top of the stringer board is in good condition, you should not need to add any trim or molding to finish off the top edge. Then very carefully paint the wall and the stringer board the same color so that the board "disappears" into the wall. Be very careful to mask the stairs using special paint edge tape so that you do not get any bleeding of the paint under the tape and onto the newly stained stairs. At the bottom of the stairs, you just need a plain piece of baseboard extending straight out from the edge of the stringer board, painted the same color as the wall. You might want to ask the floor man whether he wants the wall and stringer board painted before or after he stains the stairs. I'm not sure which is the preferred order to do that.

Rather than cardboard on those lower shelves, go to a family dollar, etc and buy some cheap peel and stick floor tiles, and put them on the shelves, so it looks nicer if someone opens the doors. The cardboard, appears to be a bit tacky. For your upper shelves, buy some contact paper, or some nice shelf liner to put your dishes and your food on. The outside is doable too. Take off the doors, and mark where they go Clean and sand them very well, fill in any dings, etc with wood filler. Resand that, so its nice and smooth. Same for the cabinet frames, and the drawers. Once they are all sanded and look decent, wipe them very well, and put them in a place where they wont get dirt blown on them, and prime with a sealing bonding type primer. Once dry, put on a couple of coats of cabinet type paint, in your choice of color. It will take a bit of time, so work on them little by little, only so many at a time. Follow the wait time between coats on the primer and also the cabinet paint can.

It is not the color of your rug, or the style of dining table you have , or the walls the wrong color. Your dilemna is that each and every one of your walls is occupied with something....a shelf, a fireplace or those two sconces. Unless you are willing to do some major reclaiming of one of the walls, you dont have any place to put a tv, except awkwardly to the side of the fireplace. I would suggest to you to rethink your expectations of your room and rethink it's possibilites. You said it was a second area, so assume you have a larger area that has a tv in it. You dont have to make a smaller area just like the other larger one. Forget the tv in there. Forget trying to stuff another tv into this little space where there really are so few options for it . So many of us spend time on our streaming devices, anyway. Maybe concentrate on making what you have as comfortable of a place to sit with your ipad as you can, or read a book, or put together a puzzle , or sit and knit, or any number of possibilities. You might also consider putting some good sized sofa table that will entice you to actually use it to lay something out on to look at or do engage with. It looks like a modern home, so why not assign a modern use to a room. So much of the past focused around either the fireplace or the tv. Things are different now. Out tech doesnt require a whole wall with surroud sound. Make it comfortable and keep it casual and do you really need another tv? Maybe it will be better with the ipad and a pair of bluetooth ear buds. You are not going to win with the battle of these walls. Dreaming of the possibilites that it could become sure seems more pleasant that scratching your head and worrying about how to work with these impossible logistics to make it into something that you dont need, and might not even really want. And, about those sconces...they are not going to go away , gracefully. Take a second consideration of them and think about what are thier best qualities. I think that they are very good for focusing light on what is below them, with the added advantage of not needing a wire and plug to travel over to the outlet and not having to occupy space on the desktop or the floor or the side table. The way that you have them is not using them to their best advantage. Do you really need the surface of the credneza lit up? Probably not. I would suggest that you think about using the space under those sconces for a sofa, or a chair, or a small desk with some drawers and a comfortable chair. Put one of these right up under those sconces against that wall and then you will be getting the best use of those sconces. Dont fight it. Find it's best and use it to your advantage. Along with the comfort , you also need some softer lighting throughout the space. Bare bulbs are almost never a good idea and over head, even recessed, is best for utilty or public spaces. You have a comfortable looking sofa and a nice comfy chair. You have some nice shelves. The fireplace is of questionable value in my opinion, but that is a different subject. You have so much already there, but just suggest that you rethink what you want from this space. It is a nice space and your home looks nice and modern and comfortable. This room could be a great casual space with a modern usage rather than another homage to the tv screen.