Yes, you need to scrape their webpages. 10 years ago when I pulled everything from my Yahoo acct, there were several choices of open source scripts which could do it.
No, it's no longer necessary to resort to scraping the webmail pages. You can easily setup a client like Mozilla Thunderbird for IMAP with Yahoo and get all your mails and folders on to it for free. I have done this recently and it has been working. Only the ad-free webmail from Yahoo is a paid option.
