The border looks like it's knit with the short edge on the needles and sewn on. I imagine it's just a yo, k2tog deal.
If I were making a patchwork blanket, I'd most likely work it all in one piece. The only real drawback might be the number of strands hanging off the back. However, if you're making squares that have different gauges, you might run into size issues.
One square might require more stithces than another to be the same size.