"a pretty, new house" sounds to English speakers as if the "pretty" is modifying the "new" instead of the "house." "A new and pretty house" is more consistent with the order in which English speakers use adjectives and prevents the "pretty" from accidentally becoming an adverb.
That's true. "A pretty new house" does sound like the house is pretty new: meaning it's "rather new" instead of being both "pretty" and "new" (which is what I think the Arabic means here). But the phrase "a new and pretty house" sounds clumsy to my ears. It's not something I would ever say. I think most of us using English (the language of a dozen synonyms) would simply substitute a word that means "pretty" but doesn't also mean "rather": "an attractive new house", "a lovely new house", "a charming new house"...
If we didn't do that, then I think we might emphasise "pretty" by altering the pauses and emphasis: so it sounds something like "a pretty... new-house". Couldn't do that in writing, of course, only speech.
Afaik, it's not a linking but a grammatical optional mark that indicates that your noun is not an object nor is possessing another nearby noun (nominative case marking). But in other threads, they say it's only used in formal speech and it's never written. There are other 5 optional possible endings, btw, but I don't remember them.
English uses "pretty" as both an adjective and an adverb, but it doesn't translate the same in Arabic. The word for "pretty" is simply the adjective. Replace "pretty" in your mind with "beautiful" and the sequence works only one way: "beautiful new house," without clumsy syntax, that is.