He sounds a bit like DS2.
He was sicky and unsettled a lot, and had a fairly impresive weight gain too, though not on the scale of your nephew.
DS2 was a sucky baby and liked to suck on the breast a lot. I also had a fast letdown and plenty of milk and he would get very tetchy after his initial hunger was sated, as he would be drowned in milk when all he really wanted was a comfort suck.
A dummy solved this problem and helped with my oversupply - his comfort sucking was not helping this at all. I know dummies aren't generally recommended this early on for bfed babies in case it hinders supply but it sounds like this is unlikely to happen.
As for not wanting to be put down, swaddling can work wonders.
This transformed my lo, and meant I could put him down, and he'd also sleep in his moses basket.
For the record, he went off his dummy at about 3 months and no longer uses it. I think the sucking relex calms down at this time and he no longer needs to comfort suck as much. My supply has calmed down too.
He's a different baby to how he was at 5 weeks, smily and settled - though still sicky and waking to feed 3 hourly round the clock - any tips on curing that one greatly received!!
Tell your sis to hang on in there - it gets better