"She wants to bring her article."

We have a dozen or so verbs without prefixes whose infinitives end in -ти. Their prefixed derivatives also end in -ти. Here is a short list, with the first person singular present tense form and the masculine past form in brackets: вести (веду, вёл) - lead, drive, run (a business), conduct; брести (бреду, брёл) - wander; идти (иду, шёл) - be going, be walking; нести (несу, нёс) - carry, bear; пасти (пасу, пас) - pasture, tend; спасти (спасу) -perf. - save, rescue; расти (расту, рос) - grow; мести (мету, мёл) - sweep; плести (плету, плёл) - twine, wattle, wicker; цвести (цвету, цвёл) - bloom; обрести (обрету, обрёл) perf. - (bookish) find; грести (гребу, грёб) - row, paddle, rake; скрести (скребу, скрёб) - scratch, scrape; везти (везу, вёз) - carry (in a vehicle); ползти (ползу, полз) - crawl, creep

No. "Он хочет принести её статью" sounds natural, but sentences like "Она хочет принести её статью" are examples of poor wording. If she wrote the article, then свою статью is used; if, however, the author is some other woman, then we'd rather name that woman than use the possessive adjective "her", because otherwise the sentence will be ambiguous.

Since "bring" encompasses the meanings of verbs "принести, привезти and привести", it certainly would.

No, it's rather 'deliver' (with a car or smth)

In the given sentence, 'her' cannot refer to another female, because in that case, we would have to say 'an article' or 'the article'.