Does the traditional targaryen name, "Rhaenys" come from the High Valyrian word, "rhaenis" meaning, "find"?
Doubt that. Rhaenis means they find. The actaul verb is rhaenagon. Plus the name was invented before the language it's probably coincidental.
Why is there a 'se' here? Usually, with two subjects, the 'and' isn't translated.
It “isn't” translated by lengthening the last syllable and shifting stress to it on the last subject. My guess is that this no longer works for non-simple subjects like the ones here (each one is a possessive phrase instead of a single word).