If you need to make the armrest higher, get a pool noodle. Cut to the right length and with a slit, you can slip it on the armrest. Alternatively, there’s pipe insulating foam available at your local hardware store - that already comes with that lengthwise slit.
Optional: Fixing the foam with zip ties or tape.
Even more optional: Add a decorative cover (...
If you can place something around the desk (top, behind, underneath and front to connect on the top again) you can then 'lock' the chair underneath the desk to that item.
I would go for a rope and a good knot the kid can not yet untie, but most people will go for the ratchet straps. It you run two side by site and knot them together in two places you make an ...
I really think that in your case, several independent desks are a better option. You will surely not do audio editing while becoming the next Shakespeare writing stuff on paper.
What I would do (and I am on the way of implementing it for my own needs):
understand which are the activities I have to do;
understand which resources (computers, monitors, paper, ...
Assuming that plywood covers the back of two long sides, but none covers the two short ends:
Position the desk so that one of the short ends touches a wall.
When you finish working at the desk, pull it away from the wall.
Position the chair against the wall as though you are going to sit at one end.
Push the desk back to the wall to trap the chair.
Consider velcro tape. Stick the soft side on your tablet/laptop and the 'catchy' side on a part of the treadmill. I have done for my phone on my car dash and it works like a charm.
You will have to consider the weight of the tablet, and have a protective cover in case it falls off.
If your equipment is expensive, consider the gooseneck for peace of mind.
I had sticky glue residue of masking tape on window and body of car due to a window replacement. Thinners for the window and then my sister surprised me by saying to use Doom (mosquito spray) . Worked like a charm .. had to soak it for about a minute ... it is also used to remove tar from body of a car.
If your child has trouble moving the chair and it is in an inconvenient location to use for climbing, this idea may work.
Place the chair wheels/casters into cups (jar lids) so that the chair is difficult to roll around. You'll have to pull it into position; but, it shouldn't be too difficult for an adult.
When the chair is unoccupied, remember to slide it ...
The second picture, the wood looks varnished, which will bloom if subjected to repeated steaming. Is the wooden top actually veneer or solid wood? It looks like permanent damage [bloom] to the varnish, which may now be penetrated, allowing limescale buildup in the wood-grain itself, making it a compound issue. I think that's a job for a sander & a new ...
The way I understand the pictures is that whatever you see is not a stain at all. The material of the furniture has wore off - i.e. it was removed due to all the humidity, heat, cleaning...
The if this is the case, then you have few solutions.
Replace the element. Contract a local furniture making company, they might be willing to help.
Live with it. If it ...
To make the monitors 'fit' above a small desk:
Don't use the feet they came with. Attach the monitors to a monitor arm. The arm is attached to the desk at one point, so you can have the monitors stick out over the sides of the desk.
This also allows you to shove the keyboard and mouse underneath the monitors when you're not using them, freeing up space ...
If you put 2 sit stand desks together. 1 left 1 right. With the controls at the middle, would that fit the space?
Custom Make Your Solution
When I wanted an inclined drawing table 20'X 3', that was attached to the wall (no legs to get in the way of cleaning) with convenient shelving over it; I hired a contractor.
A contractor can make exactly what you specify to fit in your available space to make your life much easier. In addition, a professional cabinet maker (my ...