I replaced the widows in my house this spring, and you're asking a lot of the same questions I asked.
First, the cost of the windows themselves is only part of the equation. You also need to consider the removal of the old windows, installation of the new ones, and the finish work - because chances are, all the trim, and all of the interior sills will also need to be replaced. Installation can actually be 50% of the cost of the job, and a poor installation will ruin any value you might get from buying a top-notch window.
There are a few things to consider when looking at the windows themselves. First, as you point out, is the construction. I ended up going with vinyl - again, a quality vinyl window and a cheap vinyl window are two different things - the local shop here had examples of a number of different windows cut open so you can see the difference. Cheap windows may not be insulated, or may be made up of different pieces glued together, rather than a single extruded piece.
Next, the glass. You can get single, double, or even triple panes. Some use argon between the panes, some don't - the sealed, argon-filled windows offer better insulation. Then there's the low-e coating on the glass - it can be applied in different ways, which will affect the durability and effectiveness of the window.
You need to consider casement vs single hung vs double hung. Are they on a 2nd or 3rd story? You'll probably want to get a window that allows you to clean the outside without having to get up on a ladder - most double-hung windows will allow you to clean it from the inside of the house. If you're putting windows into a bedroom, you have to allow for a certain size for egress - you may need to go with a casement window in that case.
The bottom line is, check around - get at least 3 estimates, unless you're planning on installing them yourself. See what's included in the estimate - one of our estimates included a single line item for "Installation", while another had 3 pages of details, down to the number of board-feet of trim, cans of foam insulation, and the cost of the building permit. Guess which one we went with?
You can purhcase products such as DampRid. It is availabe in various size packages and will work to passively dehumidify a space.
You do not want to use a fan or any active air mover to attempt to dry the window space. This can enable the mold to spread to other areas.
Mold is dangerous to your health and this issue should be handled soon. One point of concern is that the mold may be in the drywall surrounding the window. The mold issue should be brought up to your building manager. If they do not take corrective actions, you should speak to the local public health department.
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One way is to heat the whole house so it is above the outside ambient temperature, say 24 degrees C, then use a thermal camera to take pictures of the outside walls and roof surfaces of the house.
Those walls, windows etc that are loosing heat faster than other surfaces or parts of surfaces show up. If the camera is calibrated then it will provide a scale showing the relative temperatures.