'out' and 'in', here, refer to fashion. Things are in fashion or out of fashion but you don't need 'fashion' if it's clear from the context. Boot-cut jeans are out. Skinny jeans are in. So in a sense it means one has replaced the other, but it's in terms of what the current fashion or trend is.

‘To be in’ and ‘to be out’ are informal ways of indicating whether something is trendy or popular. Note that in written English, you don’t omit the personal pronoun. I hope you are doing well. I came across the sentence …

You have the general idea :). Bad boys and bad girls are usually synonymous with young people who pursue momentary pleasure and tend to lack maturity. The emotionally mature partner is the opposite-- a bit older, calmer, more mature. To be out or in is similar to the idea of 风行一时 - some things are popular for a while and then their popularity fades. Hope this helps :)

"out" abd "in" mean "exclude" and "include" here