I really think you need some breastfeeding support. Whilst it’s true that breastfed babies do feed a lot, including comfort feeding, sometimes a lot of very long feeds can be a sign of a poor latch that’s resulting in inefficient milk transfer. Please look up your local breastfeeding support group and go along, you can have a good chat and everyone there will completely understand what you’re dealing with.
Please, please don’t doubt your milk, or milk supply. There is a growth spurt at 3 weeks which makes babies extra fussy and ravenous, and giving formula top ups at this point will stop your body increasing your supply. I know your Mum means well but by giving him formula she’s actually undermining your ability to breastfeed.
It’s been said several times on this thread, but stop trying to put him down in his pram or Moses basket to sleep. He’s three weeks old, he’s going to wake up everytime you put him down, guaranteed. Babies need contact, they need to be held, they need to be close to us. It doesn’t have to be you holding him, your DH or Mum can burp him and cuddle him to sleep, but as soon as they put him down he will wake up. Not because there’s anything wrong with him, but because he’s a 3 week old baby, it’s normal for them to wake up if you put them down.
Set your bed up to safely cosleep, even for daytime, a nap for both of you in the afternoon can make a huge difference. Your sister is right, he doesn’t know the difference between night and day, but again, this is normal. No baby dies at three weeks old. Cluster feeding in the evening helps babies start to sleep longer at night, so again, giving formula at 8pm will interfere with that.
Finally, if you are going to ignore my advice to stop giving him formula, make sure anyone giving him formula is using paced bottle feeding. Have him reclined at 45° or laying on his side, and hold the bottle horizontal, so the test is only half full of milk. This way he has to actively suck to get milk out. The traditional hold with baby on his back and the bottle tipped up results in milk dripping out even if he isn’t sucking, meaning he has no choice but to drink it all. Babies drain bottle like this not because they are starving, but because they have no choice because the milk is flowing into their mouth and if they don’t swallow it they’ll choke!