Let's address these problems. First, let me say I started with a 2'x4' plywood table in a 4'x4' walk-in closet. This was in a 3-room (living room, bedroom, dinette/kitchen) apartment. I built two .40-size trainer planes in there. I swept and vacuumed every day, went to the porch to do major sanding, and moved to the dinette table to cover. It was awkward, but I REALLY wanted to model, so I improvised, adapted, and overcame. Since I lived alone, I was able to do pretty much what I wanted with the place. After finishing the second trainer, I moved the workshop to the 10'x10' bedroom. I had a hollow core door on sawhorses, and small oak tool table. I had a drill press and a palm sander. I worked with the door closed to prevent thr spread of sawdust and cleaned up frequently. I moved a single bed into the dinette and ate in front of the TV, which I usually did anyway. Inconvenience, yes, but it worked. My workshop now is still about 10'x10'. I have a hollow core door "spare" table, and a 5'x3' workbench. I have a Dremel sander, 8" band saw, jig saw, and drill press in there. There is a dedicated tool table. Lots of storage space in cabinets and under the benches. I clean frequently and still do major (palm sander) sanding outside. I've built several 6' wingspan models (two triplanes) in there and am currently working on a 96" span old-timer. I have no major problems building in there. I have to be careful when moving the plane parts around, and have to not let the clutter and trash build up, but it works. It can work for you, too.

The one BIG advantage of a small workshop is it forces you to develop good building habits of neatness, cleanliness, and efficient storage.

Unless someone has access to a garage or a workshed, it is very difficult to build a plane.
See above.

But I can't put any power tools in the room (belt sander, drill press, etc.)
Why not? You read what I have in my workspace. All my tools are on stands and moveable. They stay stored until I need them. You don't need big power tools to build R/C. A table-top drill press, 8" band saw, and a Dremel belt/disc sander cover 95% of my power tool needs. I also have a hand-held battery drill and two Dremel tools.

I have to go outside in 100 degree Texas heat to sand, because other wise it goes all over the place ( I share the room with a computer and washer/dryer). It's carpeted, so I can't easily sweep out the debri each evening. Etc. etc. etc.
I favor outside sanding anyway. The lighting is much better and you can see every little imperfection in the wood. Go to Harbor Freight, or another wholesale tool house, and buy a small dust collection system. You can pick one up for less than $150. A visit to the shop vac department of your local Lowe's or Home Depot will get you the nozzles and adaptors to fit your various power tools. As for vacs, get a GOOD shop vac. You rate vacuums on now many amps the motor draws. The more amps, the more suck. Get the vac and use it after every building session. It only takes a couple of minutes to run over a carpet with a 18" carpet wand fitting. You can also build walls and folding doors around the W/D combo. It's done all the time for many reasons. "See, honey, I built this to help protect your expensive W/D."

See, it CAN be done.

Dr.1