At 63 he is probably just used to being alone. Public affection is not something that everyone likes to show. Not and excuse but he may need time for somethings.
You need to talk to him, if they are not his kids but he helped raise them or spent a significant amount of time with them he may be attached. There is nothing wrong with that either. As long as it is just a parental type of relationship. Again you need to talk to him.
If he was previously married you would have had to show the divorce decree at the interview and he would need it again at AOS.As for her using his last name, it's most likely she just didn't change it assuming FB/social media name? You can use what ever name you want on the internet. It can be a made up word even.
Honestly I think you might need to talk a lot more.
The only way you can stay in the US legally is if he agrees to not pull the AOS, and that is very unlikely to happen.