Duality

Oooh, time. Great stuff. Definitely one of my top four favourite dimensions.

Alas, I personally know of no solid books on the topic to recommend. Wikipedia, however, actually works fairly well as a technical source on time. I know the site gets a lot of flak for being unreliable and completely publicly editable and so on, but in regards to the science behind how time works, as far as I know, it's just about as good a tradeoff between accuracy and accessibility as you can get on the subject - it's the more subjective and controversial topics on Wikipedia that are primarily to be mistrusted.

The article it has on time has a lot of concepts packed into it, and there are plenty of links to additional articles explaining many of the concepts more in-depth. As a matter of fact, there's even a list of books about time at the end of the article, including the one by Hawking you were presumably alluding to:

I've never read any of them myself, but they all look thought-provoking enough that I'm interesting in doing so now. 

As for the 'conical graph representation of time' you saw, that would be a Minkowski spacetime diagram:

You're at the centre of the diagram, with time as the vertical axis and space as the horizontal axis, and the two cones (here simplified into triangles) are the conceptual paths of rays of light, travelling directly towards you from the past and then passing through your location in the present to travel directly away from you in the future. Since nothing can travel faster than light, everything outside of the spacetime cones/triangles cannot affect you (it's travelling at the speed of light away from you or it's just too far away to affect you in the present moment). It's a diagrammatic summary of a lot of core concepts in special relativity.

That's all I can currently think of to refer you to, but if you have any questions I can always make time. 

What, and technical theory on the existence of Time isn't relative or controversial? Can probably form a quick line of teachers that would be more than willing to take turns slapping you silly for daring to mention Wikipedia! But I will, I will.

 ...Heidegger?! That's... PHILOSOPHY! Squeee! 

 I actually was making little squeaks while noting down that list! ..though maybe that can also be attributed to the three slices of cake 🎂 I just had. ...among other symptoms, lol!

Einstein's Dreams...? Hmm, do remember reading somewhere that Einstein got most of his theorizing done by dreaming. By imagining how it would be like to be the supposed particle in question. ... to redirect back to what we may have talked about before, of the links betwixt a Scientific Mindset & a Creative one.

If I'm reading that graph right... then it won't imply that the more Space, the more "Present" Time? Ah, am familiar with the concept of, say, the light of a distant star reaching us well after its origin ceases. Do suppose it would be right to say that Time & Space are "Married" con..... cepts.... 

 Hrnk!

 I... guess...th-there goes my idea of having a Theoretical Concept Waifu....       ...feel a trifle faint now~

Technical theory about time is less controversial than, say, the life of Osama bin Laden or the Holocaust, put it that way. People tend to direct their energy almost exclusively towards arguing about things that aren't the core concepts that constitute life itself, for whatever reason. On that note, I concur entirely that philosophy is squee-worthy. 

Creativity is a good quality in pretty much any field, let alone science. If you have a good imagination and a logical mind, there's not much your brain can't do for you.

I wouldn't say time and space are married concepts, though. More like a family consisting of the three Space dimension-brothers and their enigmatic and more mature sister Time. Your waifu isn't already claimed, you just have to stay on her siblings' good side.