For the first part, I'm gonna put some girls together because there may be some differences but it's usually similar to each other.
The three Regi: the MC cleans them even though they don't get dirty on the ship often the MC likes to clean them frequently to make them shine, even though they don't emote he likes to think they enjoy it.
Latias, Latios, and Rayquaza: they like to fly around on top of the ship Rayquaza doesn't fly around the same time as the twins but it's the same between the three of them. They fly around at the top of the ship and the MC sits on top of the roof chatting with them and just watching them fly around.
Lugia, Kyogre: The MC spends time with them in the pool them do like being on the water so they stay around the pool when they have time, but both of them are in the pool at different times of day because they don't like each other and the MC doesn't want them to fight besides that he spend time with them. He's either in the pool or beside the pool just hanging out and chat with them.
Articuno, Zapdos: preening (straighten and clean its feathers with its beak) the MC helps them do that the two of then says it's feels like taking a haircut. The reason why these two are together is simple I couldn't think of anything for Zapdos
Next is the girls by themselves and what the MC does with them
Moltres: the MC rates her roasts and gives feedback And helps her come up with new ones
Mewtwo: the MC showers her with praise because she's the type of person if she gets three compliments, she gets flustered and it's very cute and she doesn't have the best self image of herself so the MC make sure to complement her often to try built that self image up
Mew: they play games or what she calls games like hide and seek catch the ball or her favorite where did your pants go where the MC has to find his pants because she head them somewhere he has already lost five pairs of shorts to this game and he refuses to lose anymore
Raikou: they go for runs around the ship the MC does his best to try to keep up with her, and even though she would never say this to him she slows down a little bit so he can catch up
Entei: they work out together. The MC has to stay in shape so he can go get more legendarys because he has to do a lot of work just to get to one of the new legendarys and Entei said she will be his personal coach and trainer
Suicune: they go for walks around the ship. They talk about all sorts of random stuff like clouds waves trees, and about how that guy just got smited in front of them. That is still a weird one
Ho-Oh: the MC listens to her stories because she has a lot of wondrous tales about all sort of things, like what she did in the early years of her life when she first help the three legendary beasts, all sort of things
Celebi: the MC questions her about history really because it's the only thing he can really understand about her because she's a little complicated to understand with the whole time thing but she does like answering his questions
Groudon: the MC take sunbaths with her because she is still just a massive lizard, so she likes taking sunbaths near the front of the ship because Rayquaza is in the middle of the ship most of the time and Kyogre is usually at the back of the ship when they're taking sunbaths together, they just chat casually about things and the MC does want to get a tan, but he can never get one curse his ditto DNA
Jirachi: they take naps together. The MC has quite a busy life dealing with all the other girls going out to get new legendarys having sex so a lot of times during the day he just takes naps usually with Jirachi in the same room or on the same couch or near each other or she sleeping on top of the MC she is a little heavy, but he's fine with it like having a weighted blanket
Deoxys: they stargazing together during one day when the MC was having troubles getting to sleep he decided to go for a walk around the ship then he found Deoxys sitting down, looking into the sky to the stars the MC sat beside her and they watch the stars and silence ever since that day they had been stargazing together for quite a while