lolno
Do you go easy on beginners?
Difficult one, really. It's a good way to keep total beginners interested and help them improve, but with a few caveats. First, only go easy on them if they want you to. Deliberately making blunders may only patronise someone who's trying their hardest and wants a challenge. Second, they may become reliant on you pointing out mistakes, rather than finding them themselves. And it's probably not a good idea to do this online. Mild-mannered, friendly competition is painfully uncommon. If there's no other option, use some kind of voice chat so communication is easier and less likely to be mis-interpreted.

It depends. You say your brother has only recently gotten into chess, so he can just as easily fall out of interest, and as a gaming nerd, beating people mercilessly is
1. Not a good way to make friends
2. A very easy way to make someone quit something
Who would have known, right? I personally would go easy on them for a while to see if they would stay interested in chess past like a week or two, then gradually start trying. In the end, though, it depends on what your brother is like and what his learning style is. I have a brother and mother who both know the basic rules, but nothing beyond that, and I occasionally beat them up when they decide to play, but since they aren’t serious at chess and probably will never be, it doesn’t weigh on my conscious that much.

Played a guy at work otb with no queen and still crushed him lol. Id give odds so people dont end up hating chess. What iv noticed tho is most people who say they play chess and we sit down and have a game i notice within the first few moves if there 400 elo and they dont wanna play anymore :(
Be merciless, no just kidding. It's your brother and you don't want him to lose interest in the game so if he's playing badly why don't you play over the games after you finish and highlight some of his mistakes. I suppose that this can be taken one of two ways, it depends how your brother sees it, good advice to help him improve or mocking his play. Try a subtle approach firstly, review a game later and ask him what he was thinking at a particular point in the game, you will probably have a much better idea how he'll view any kind of advice by his response. If he picks something up and launches it at you, it's probably not a good idea to offer him any more advice.

My brother recently got enthusiastic about chess and got on chess.com. We’ve played a few games and I really, really enjoy it because he’s incredibly busy and this is an excellent (if small) way to stay connected.
But here’s the thing: He’s really not very good and the games have been bloodbaths. I’m no Kasparov but I am just obliterating him, even though I’m a very casual player. I tried giving him material advantage (down a knight and pawn) but I sacked him in that game, too.
Now we are playing a new game and he just left his queen hanging on like move 6. Do I take it? Or pretend I missed it? If we were in person I would let him take it back or warn him as he started to withdraw his fingers or something, but it’s chess.com. I don’t know the best way to help a beginner. Is playing down to a new player doing them a disservice? I really don’t want him to get frustrated and quit chess, especially because this is a good chance to stay connected.
What would you do?
Tl;dr my bro is a 750 ELO noob, do I ignore obvious mistakes to help keep him interested in the sport?