So, on the forum we can buy blog submissions usually with 3 links in them. Is useless for all 3 links in the article to have the same anchor text? In order words, is it better to have different anchor text for the three links or is it better for them to be identical?
It's better to have them be different. Use your primary keyword on all of them, and mix up different keywords to complement that.
Ill give you a tip, make those 3 links have different anchor text and point to different pages in your site (deep links) too . Thats how you will get the most out of every submission.
another question, let's say you want to show up for a search for "hammer" and "screwdriver". If you start submitted directory listing as "Hammer | Screwdriver" ... the anchor text would clearly be hammer | screwdriver....so you google's algorithm make it so that these would could as backlinks for the keywords "hammer" AND "screwdriver" instead of the phrase "hammer | screwdriver"
Just repeating what's been said above - it's getting deeplinks to a site that is hardest to do and very important, and paid blogposts are one of the best/easiest ways to do it. Important why? Because it helps stop internal pages going supplemental, and also it better mimics 'natural' linking - where people just link to any page in your site that they think is interesting. 'Real' links are not usually to a site's homepage, but to an article or page within a site.