Can other couples get ability interactions like Xayah and Rakan?

No, because its terrible design.

If one is ever strong, he/she gets stronger with the other, which makes it worse. God forbid if both are strong individually.

That doesn't encourage diversity. It smothers it. Interactions? Sure. Having it affect gameplay? Fuck. No.

Xayah/Rakan gameplay interactions shouldn't exist in the first place.

Guess it would be very platitudinous to write Taric + Ezreal

I think it makes pro drafts more interesting, and there's room for a little more, but too much can mean that pro drafts become a fiesta and games are decided at draft stage, which no one wants to see

If Ashe drops below 25% HP while Tryndamere is within 1500 units, his rage bar fills instantly. :D

Yeah, as others said, that's definitely a balancing nightmare.

Maybe you could share the "Lover's Leap" passive (sharing the recall), because it presents a connection but with minimal gameplay influence.

Anything more and it becomes a problem. Take Rakans E, for example. He basically has a long-range 2 second recall if Xayah starts it and he dashes to her when it almost finishes. The gameplay problem here would be the (long-range) dash, not the recall itself. (From the couples you mentioned, Trynda and Lucian both have dashes but I don't think they would be a problem.)

I just want a Veigar and Lulu thing. No buffs. Just want them to be a thing and have a valentine skin (maybe they were each others outfit while in their color scheme OR wear something matching)