You can't use bedsheets as quilting fabric as the weave is too tight. I use them all the time with no issues. I just don't reach for 1200 count Egyptian cotton ones.
The large spools of serger thread are a weaker cheap thread and can't be used for quilting or general sewing as they'll break more easily. I've tested mine by sewing a scrap piece of fabric and tried to pull it apart...and tried, and tried.... and I also tried to melt the darn stuff while ironing it. Actually held my iron in place for about 20 to 30 seconds (which I would never normally do) and it held beautifully so I definitely use polyester serging thread to piece and quilt.