I'm quite new to indesign, so bear with me.
I've selected a color with the eyedropper tool, and once I am about to draw using the rectangle tool, the color switches to grayscale. How do I change this?
You are selecting the color before drawing the rectangle , do vicecersa , means first draw the rectangle (it will be filled with the gayscale) thne pick the color with teh eyedropper tool and apply on the rectangle
Which tool are you using? The rectangle tool with the X in it is called the frame tool and does not respect a preset stroke or fill -- it is hard-coded to have no stroke and no fill (even if you add them to the Basic Graphics Frame object style). If you use the open rectangle, it should respect whatever colors are set before you draw. If it does not, see Replace Your Preferences