My cat growls and paws at new cat. Is this normal? Should I continue?

That's ok, this can happen. Resident cats can have disagreements with each other. You may hear some howling, hissing, and growling. Again, this is normal. You might even see them swipe at each other. I would only intervene if the fighting becomes aggressive, they are biting each other and hitting each other. Otherwise, leave them be to work it out on their own. I hope this helps.

It is OK behavior but not great. I am worried that this could escalate into a serious fight. I suggest you try using some Feliway diffusers in the house and do some environmental enrichment for them. Those two things should help. ( https://www.feliway.com/us/Products/FELIWAY-MultiCat-Diffuser ) ( thedrakecenter.com/materials/environmental-enrichment-indoor-cats ) ( https://www.youtube.com/watch?v=AejmrLa_Cs4 )

That actually sounds like very normal behavior for a cat who is adjusting to a major change. It sounds like Arlo is working on getting comfortable in his new environment but isn't so sure about the humans there yet. I would recommend giving him lots of space, not taking the growling personally, and giving him time (probably a week or two, maybe even months) to warm up. Let him be the one who chooses to interact with you, not the other way around. you can definitely use food and offerings of toys to try to entice him to come interact with you, but it should still be his choice. Congratulations on the new addition, I hope he settles in soon!

Unfortunately it's very common. It means you need to rewind a bit and introducing more slowly. It can take months to fully integrate a new cat (and sometimes it doesn't even work at all). If eating in the same room was fine, go back to that for a few weeks, but no free roaming.

This sounds like a typical play behavior. In general watch for signs that one cat is trying to avoid the other cat. Watch for the cats hissing at each other. Watch for any signs of intentional bites or scratches that leave marks. If the cats are willingly interacting and you don’t notice any hiding or avoidance behaviors, this is likely consensual play. You may also look into reading a few books about cat behavior as it is not only informative but also fun! I hope this helps.

While it's fine that they growl and hiss at each other, as they are letting this new cat know they don't appreciate his presence on their territory, you don't want it to escalate into aggression and one of your cats get injured. I would keep an eye on their interactions as best you can, and step in if it appears that anyone is going to get aggressive.

Most cats will settle down within a few weeks. Kittens do play rough and it can be hard to tell. If they willingly come together, play willingly and you don't see any bullying behavior (avoidance, hiding, arching the back and puffing up the tail) they are likely playing rough. If they play too rough they could injure each other by accident so continue to separate them when not supervised but most kittens will not require this. Giving each kitten one on one play time with you to burn energy, feeding out of a food puzzle and providing cats trees/other environmental stimulation can also help. Continue the current therapy as well. I hope this helps.