I usually scan at 600dpi and then resize the image back to 1000 x 1000 px (for covers) before posting. That allows me to do any necessary touching up at the higher resolution before the resizing. It seems that everybody has their own way of doing it. My advice is to find out what works for you with the hardware and software you use, and gives you the kind of quality you're comfortable sharing with the world.
I've done them both ways, but am moving more toward keeping the pages together. I figure if someone wants separate images, it's easier for them to extract them out of the combined image than it would be for someone to stitch individual images together. Besides, it's (slightly) less work for me that way, and I'm basically lazy.
Under Windows I use a free program called Paint.net (https://www.getpaint.net/index.html) to handle all the scanning, touch up and resizing. I find it powerful enough for my needs and pretty easy to use. And the price was right. Your mileage may vary.
I've done this a couple of times by scanning partial images and then stitching them together (in Paint.net) to get a single composite image. One that comes to mind is the booklet for Prairie Noise - Play This Disc. I can't remember if it was 4 or 6 scanned images that I stitched together, but the final image is here.
There's a fair bit of work required to get a decent result, so I don't do it very often. Did I mention that I'm basically lazy?
One of these days, I'm actually planning to try using my digital camera and (soft) portrait lighting to try capturing the oversize images that way. Not sure if it will yield the desired quality, but it's worth a shot because it will be a LOT easier than scanning and stitching. If it's even close to a good result, I may try using a non-glare sheet of glass (or plexiglass) to press the poster flat for the shot.