Is my saddle at the correct position? I am trying to determine if my saddle is setup right. 

In the picture below, my feet is at 9 o'clock and the improvised plum line that starts under my knee cap (hard to see, spot the white line against the bottom tube) is not going through the ball of my foot or near the pedal.

IIRC, the line should go through the ball of my foot and pedal spindle right? In this case, I need to back up my seat?



Edit #1

In the hopes of adding and clearing this post up a little, here's the other screenshot that I had taken with my heel on the pedal, to show the height component of my saddle:


I thought the height was ok.

I'm trying to solve an issue and wanted to tackle each bit individually starting with my saddle setup.

The issue that I'm trying to solve crops up after some time on the bike. It seems to be related to the amount of cranking going up hills. It varies in time and distance. If I concentrate on being in a lower gear than I want, and patiently go up hills, I can delay the pain from appearing.

The pain will start on the back and outer side of the knee, at the very top of the right calf. It first starts off with a warning, a dull pain. Then, I need to push the bike up the hill due to the pain when I crank on the bike. I can do flats and downhills ok.

IIRC, this is entirely related to my cleat positioning.

So far, I have been moving the seat around a bit to test to see if it made any difference. It doesn't. This post was to take the seat out of the equation so that I can move on to other things.

Edit #2

For the sake of completeness, I'm adding new snaps featuring more legs :)





Edit #3

IMO, it seems highly likely a cleat issue. However, wondering out loud, could my issue be related to lack of mobility perhaps due to some muscle groups not firing properly? (Glutes maybe?)
Not enough information can be seen in your picture. 

What you are looking for currently is a red herring. Whether a line from your knee cap does or does not cross any point on the shoe or on the pedal is strongly affected by the seat tube angle (and also the crank length). In the extreme case of a recumbent bike there is no way those could intersect - but the position setup is no less important there.

And not just the (for some to far-fetched) recumbent bike example, check this racer



(from https://www.slowtwitch.com/Photos/Products/Winners_and_Losers_Helmets_4712.html)

Due to his seat-tube angle the guy cannot ever fulfil the rule.

What you should look for are the smallest and the greatest angle your knee makes. For that you need the pictures of you pedalling made from higher point, best completely perpendicular to the knee. That's what bike fitters are looking for (among other stuff). A bike fitter can do that for you or you can try to do that yourself, there are instructions available on the internet (e.g., https://www.ludd.ltu.se/~torger/bikefit/ - the site also discusses the KOPS method you have used, for most common bikes and average riders it works quite well but the site does also offer better methods).



(from https://www.ludd.ltu.se/~torger/bikefit/)

To answer your actual question about your own position, taking your edit into account: I cannot see any obvious problem in your seat height and I would indeed try to search a problem in the cleat position. You can also try flat pedals for a while and check whether they change your situations. The may help to narrow down the problem. It is less easy to assess your forward-back seat position but considering the KOPS method it is not way off but may be slighly forward. Or it may not, I would still try to measure your min and max knee angles, it is more accurate and considers the actual piece of your body that hurts.

Ad Edit 3: It can and it can be due to many various gate issues. For example, I have problems with my hip and knee orientation and resulting duck feet which is worse on the right leg. Some issues are more obvious and some less. A professional eye will know better (a physiotherapist or bike fitter, but not just any, but some that actively deal with similar problems). Consider cleats that allow some float and try to find out what Q-factor may be the right one for you.