Basically, Google shows the autocomplete suggestions whenever you start typing anything into Google search box. It is in Google's best interest to show the most relevant keywords in the autocomplete suggestions. Keywords that would help Google to retrieve the most relevant websites and help users find the most relevant content for their search query.
Does this mean that Ahrefs gives false difficulty scores? No. It just means what in Ahrefs's opinion, building the recommended number of links to your page will influence all the other factors enough that you will rank. Building 10 links to your single page will increase its page authority and your domain authority. You will be likely to end up closer to page 1.
Another feature of Ahrefs that could potentially help you take your campaign to even better heights is their content gap feature. It gives you the option to check which keywords your competitors are ranking for so you can stay one step ahead at all times. Basically speaking, Ahrefs gives SEOs the ability to overtake their competitors through knowing which keywords to target and focus on.

Google cares about Content first and Links second when it comes to how it ranks a page within it's results. This tool allows us to see where competing domains are earning links and insights into the specific content that attracts links for the competition. This insights assist us in creating an actionable strategy for our clients using a CRM such as Buzzstream to import data into.

Of the three popular backlink reporting tools (Majestic, Moz, Ahrefs), Ahrefs provides the most useful link data. Even in other areas of SEO, Ahrefs seems to always keep their toolsets fresh. They continually add in useful tools and features that make other software suites less relevant. The most recent addition is their site audit tool which provides a beautiful visualization of technical site issues.
What would be the purpose of/reason for moving back to a different url? If its been a few years, I’d leave it alone unless you watched everything decline since moving to the main url. Moving the forum to a new url now would probably be a bit chaotic, not only for your main url but for the forum itself…. Only reason I could imagine myself moving the forum in this scenario would be if all those links were really awful and unrelated to the url it currently sits on…