Alicornutopia

So, I assume most of us have various proper nouns in our settings which are supposed to be from fictional languages, each presumably with its own phonemics and often no in-universe Latin alphabet orthography. When you write such words, do you use approximate English orthography since the rest of the writing is in English, or do you use a mostly-but-not-entirely-Latin-based language-specific orthography as (I think?) is generally done for real languages, or do you do something else?

My conlangs are often like little baby characters; they'll tell me how they think their words should be pronounced given the arrangement of letters involved. When I can, I try to tweak the spelling so that a native English speaker will have a good chance of guessing how it's supposed to be said, but sometimes the conlang has too many opinions and I have to just go with what it tells me. When I do make cosmetic spelling choices in English (e.g. K vs C), the language will make me come up with a reason why that transcription would be sensible as soon as anyone squints at it. (This, incidentally, is how Suranse ended up with an alphabet song - the language wanted me to give it an alphabet in order to justify my spelling of 'Ceir'.)

Varies. I usually start by spelling things in a way I think will elicit the right pronunciation, but if the first words from a source suggest a rule I may run with that even if English speakers wouldn't naively pronounce later inventions right.