For example we have 27 articles, and 440 tags.... that should give you some insight as to the website I'm trying to clean up....

With this information.  I can say that I would delete all 440 tags if this was my website.  I would not need to think about it.  These pages are going to be duplicate content and dangerous to the health of the site.  They will also be a power sink.

One of my site has a million of these links.  No kidding.

I had nothing to do with these links.  They are simply gifts from blackhats.

The site is very healthy, has kickass rankings, does not have any penguin or unnatural links problems, so I am doing nothing about those links.

Will that count as traffic from Google so it will increase the CTR from Google?

It is a good bet that Google uses multiple metrics that confirm one another to be sure that their rankings are not manipulated.  That traffic would also need to explore deep into the site, talk about it in social media,  write about it on blogs, return many times over a long course of time by typing the domain name into search boxes or the address window of the chrome browser.

So, instead of trying to fool google, just improve your website so that these things happen on their own.

I really enjoyed Robert's answer because we all see so many of these DA and PA envy questions.

To build on Robert's theme of "leverage your advantages" - these directories are usually built by people who know very little about your local area or industry.  They are also generally cookie-cutter sites built by factory workers who live 1000 miles away.  For those reasons, it is often very easy for a local expert or an industry expert to build content that is vastly superior and to provide a landing page experience that impresses the visitor enough that he will share it with others.  You probably also know the visitor better than the factories who build these sites too.

Put some time into your content and presentation.  Winning there can significantly improve the success of your page in the SERPs.  It can also significantly improve your chances of attracting the searcher to your business instead of the business of your competitors.   Show your expertise!

Most of my work is writing articles that take between three days and a week to author.  I also have employees who assist with these articles by taking photos, making graphics, doing research, collecting data and posting them to websites.   Some of these articles attack very difficult keywords.

After doing this for about 12 years on the same website, I still don't know how these articles are going to rank.  A year or two after posting some are on the first page of Google defeating popular websites that surprise me.  Others, perplex me because I am being beaten by pissants - in SERPs that I would judge to be much easier.   I suspect that semantics, keyword diversity and titles that elicit clicks help the pissants beat me but I don't know for sure.

I can't predict how my own rankings will turn out on a website that I know well, in an industry where I have worked for 40 years and against competitors who are often people who I know by name or are even my own customers.  The SERPs can be very difficult to understand.  One thing that I will say with confidence is that DA and PA explain nothing and give zero guidance in winning a fight.  They count as zero importance in my decisions.  I can't even tell you those numbers for my own websites unless I go look.   That's how little attention I give to them.

Lower case first letters are easier read by the average person.

So, I am starting to write my title tags with the main topic with upper case first letters on the left, and then the rest of my title in lower case letters on the right.  That lower case content is focused upon appeal, value, popularity, surprise, inquiry, or panache.

If I see a study, I'll post a link here.

It was similar to a Q&A.  There was a single sentence question and a paragraph of hidden answer.  This page had a LOT of questions and a tremendous amount of keywords in the hidden content.  Thousands of words.

The long tail traffic tanked.  Then, when we opened the content again the traffic took months to start coming back.  The main keywords held in the SERPs.  The longtail accounted for the 80% loss.

Most universities are going to list the scholarship on a page of their website that contains information about the scholarship and other related scholarships.  They might say that the scholarship is funded by a specific company but if you think that you are getting a link out of it that is being presumptuous.  They are probably NOT going to link to you.  Look at their scholarship pages.  My bet is they are NOT linking out.

So, if you want the scholarship to get big buzz it better be a really big prize and your website needs to be the exclusive source of the full details about who is qualified to receive it, how to apply, and if it is awarded on the basis of competition or merit, how the winner of the scholarship will be determined.

How much should the prize be?  Before I answer, I will say that you should be in this for helping people more than for SEO.  I'd start at $5,000 or more.  With a new prize awarded each year.  You can get a bit buzz with a scholarship of that size.   You will get zero buzz with a $500 scholarship.