Generally speaking, a room with a light-colored ceiling will appear taller than a room with a dark-colored ceiling. However, in a really small space painted in a darker color, painting the ceiling the same color will make the border between wall and ceiling disappear, making it more difficult to gauge the ceiling height by sight.
A related technique for rooms painted in "warm" tones is to tint your ceiling paint two shades lighter than your walls, but in the same basic hue. This will blur the line without creating a "closed-in" feel that a darker ceiling can create.
Using vertical stripes on the walls will draw the eye up and down and will make the walls appear taller than they really are.
You can also cheat perspective a little by blurring the line between wall and ceiling. Painting a gradient between the wall color and ceiling color, that begins on the wall and ends on the ceiling, will give a somewhat forced perspective that makes the room look taller. Similarly but easier, painting a border the same color as the dark walls on the white ceiling will give an impression that the wall continues slightly higher than it really does before the ceiling begins.
One last thing; while the recessed lighting stays out of people's way, it won't illuminate the full 180* sweep from the edge on one side of the ceiling to the opposite edge; you'll get a band of shadow caused by the angle that the light is recessed into its can or tray. This can bring down the perceived height of the walls. Try filling the room with light from other sources, like wall sconces or table/floor lamps, to put light up along the walls filling the shadow.
Mold goes away when the water goes away, so unless your toilet is leaking again, you have some other source of water or leak on the upper floor. This could be any number of things, even things not plumbing related, like water getting behind the siding, or a leaking roof with water running down the inside walls. As far as killing the mold that is there, I wouldn't waste my time. If you don't correct the water problem then the mold will return very shortly.
I need to figure out if there's still a leak or some kind of humidity problem. Is it safe to assume that because the problem got worse there is? Should I try to find the pipes and see if they're leaking?
Since you have had issues with the toilet in the past that would be the first area I would check. If the drain pipes for your upper floor are leaking then I would expect to see discoloration bleeding through the paint on the ceiling and the walls. If this turns up nothing then in the hole you have already cut, I would get a professional moisture detector device like the one a plumber would use.
These can help detect moisture and humidity in the air which can give you clues if you found the potential problem areas. Don't buy a cheap one because they don't work very well, I would instead see if a rental place will lend you a good one.
I think I'm seeing some black wood in there (need a better flashlight!).
This doesn't necessarily mean anything, it could be discoloration from previous water damage.
I would still like to hire someone to fix the plaster ceiling. Is it going to cost a huge amount extra if I cut through the mesh and they have to replace some of it? Does area make a massive difference in price for that kind of job? For what it's worth, I'm fine having drywall put up instead of plaster.
How big is the hole that you had cut? You can sometimes repair a hole by cutting a small piece of drywall and fitting that back in place, then using some thinset or spackle around the edges. Sand and repeat thinset or spackle two or three times until you have a smooth paintable surface.
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That's called a drop-ceiling, or a suspended ceiling. It doesn't have to be "justified". It's one of several choices with many advantages and disadvantages. If you damage other types of ceilings, you'll spend hours speckling and sanding and painting them to repair, whereas with a drop ceiling you throw the tile away and put a new one in. They can leak air/breathe a bit, so you might not want them between a living space and attic.
A solid ceiling will usually be 'higher' than a drop ceiling because you don't need the clearance to install tiles and suspend the frame.
If you haven't looked at everything above it you should before considering replacing it with another type of ceiling. There's probably a good reason that it's there. Perhaps it conceals beams or ductwork.