Hi Vincent and welcome to the Q&A Board. Glad you're enjoying the site.
I'm going to reply very generically and hopefully some of the mods who use dSLRs (I do not) can answer more specifically next time they come by.
For the types of shots I am taking, (considering the windows and how they can wash out if the shutter speed is too slow), what settings would be best in this case, in general?
There are so many variables that could influence settings, such as the time of day you take the photos and room lighting, that it's difficult to say what would be the best settings. But since you no doubt want everything to be in sharp focus, you need to use a mid to small sized aperture to get maximum depth of field. I would also try to shoot at the widest angle to help keep deep depth of field.
Plan on using a camera support, such as a tripod, if lighting is low in order to prevent camera shake. If light is low, use the highest ISO setting that produces the least noise, perhaps ISO 400 or 800. sDLRs are much less prone to noise than non- dslr cameras.
Don't forget to adjust white balance settings to match the main source of light in the room.
Should I use the maual setting or choose from P, TV, AV or Auto?
If depth of field is important to you, I'd use Aperture Priority (AV) mode.
In any of these cases, sometimes the flash will fire, others it will not and some times, the camera won't even take the picture...it won't fire and I'm not sure why. What would cause this?
Two things come to mind: Check if the batteries are fully charged. If that's not the root of the problem, is this happening when you shoot facing a window with outside light coming in? If so, use forced flash if you have that setting.
There are lots of tips in this article about digital photography and cameras for real estate agents. It includes information about such things as fill flash and best time of day to shoot interior photos so windows are not washed out.
http://www.digicamhelp.com/digital-cameras-and-photography-for-real-estate-agents/Related reading
Digital image noise: http://www.digicamhelp.com/what-is-digital-image-noise/index.htmISO:http://www.digicamhelp.com/advanced-digital-camera-settings/iso.htmDepth of Field:http://www.digicamhelp.com/taking-pictures/depth-of-field.htmAperture:http://www.digicamhelp.com/advanced-digital-camera-settings/aperture.htm