Hello and welcome to the site, some great advise already given and I agree with.
Dont worry its not too late - I am still working on introducing a stray to my household and he's been with us over 2 mths
but that only cos he's a bit of a fighter and torments one of my younger cats, so I am taking things a lot slower than usual. He wasn't neutered when he arrived so we have had that done, which has slowed him down a bit....
Cats just need to get to know each other bit by bit
they newbie will have smelt all a bit strange to the existing cat and of course, it will have seen the newbie as a threat to the territory. Newbie will have been all confused about its new surroundings - a bit like first day at school for kids
I think it is best to dedicate a room for the newbie - it doesn't have to be a fancy place, but as long as it is safe, warm and has all the necessary things for a cats needs, it will be fine and they do settle into a routine quickly.
Routines are important.
I kept to a strict bedtime for my terror Teddy, he always went to bed at 10.30-10.45 I got him to go there with a treat of kibble, just rattled his bowl and he soon got the hang of it. I stayed with him to settle him in the 1st few weeks that he was with us but he soon knew the routine.
I alway fed all my cat together at the same time - but Teddy's was a bit away from the other as I didn't want to upset their routine either. If he tried to get the other cats food, I just gentle picked him up and moved him back to his bowl. If he finished I then let him go outside - all my cat are indoor/outdoors
If Teddy got into any squabbles he had time out - not as a punishment . just some quiet time. I'd never shout, but just calmly and firmly say NO, pick him up and take him to his room, again he soon knew and used to run onto his bed. I'd let him out after an hour or so and all would be calm again
Well food time is a lot less stressed now as Teddy realises he is going to get fed
hes calmer cos he's been neutered but he still has quiet times now and then.
Well sorry to ramble, but I thought relating my experiences would help.
I am sure you can come up with some solutions and with a bit of effort and patience I things will settle
keep us posted