Now keep in mind that, based on their stated crawling guidelines, the stronger links from stronger sites tend to get crawled more frequently so the spammiest of the spammy link approaches might not get picked up on. For that level of deep research a historical report from Majestic SEO and a link status checker, like Advanced Link Manager, is likely a better bet.
The backlink index is one of the best too though at the time of writing, Moz has just improved their index. Regardless of index size, which theirs is large enough, the type of data they provide is the most useful. The broken links data is probably the most useful that isn't easily matched by other tools. Additionally, going back to the content explorer, you can find unlinked mentions, a feature that appears to have been removed in Moz's "new" tool (I may just not be able to find it).
As of September 2014, YouTube's own keyword tool stopped working. It was moved over to Display Planner's AdWords video keyword suggestions. To use it, you need to have an Google Ads account. Just like the non-existent YouTube keyword tool, it was created to facilitate paid video and ads promotion. Which is why keywords that you will find there might not be closely related to the topic that you want to cover.
Depending on the plan, you are only allowed up to 100 domain searches a day. If you purchase their top tier plan you only get double of that. Sometimes it can take you several days to do certain types of research. This can start to get a little bothersome as we work with several clients and all of them need to use this software to make sure everyone is getting the best work that we have to offer.
One of the things that AHrefs is best at is helping with a content marketing strategy. Though it's best known as a backlink index (which it's great at and I'll get into that), coming up with good content ideas is one of the things I get the most use out of it with using the content explorer. I find articles that do well for the topics I want to target and it's clear what already resonates with your audience which is powerful.
AHREFS is certainly a great tool for bloggers and internet marketers. You have explained every functionality in great detail. I liked the link intersection part. It provides ou with a great opportunity to get backlinks from sites which are usually linking to your competitors. Further, its adds to the fact that these types of backlinks would be easier to get as compared to the ones that we search manually for any website. Plus, these would be niche specific too!