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When you first put the car together there's a set of absolutely invaluable charts going over turbo spooling, braking wear, steering control and what not. When you test the engine though that diagram is completely lost and I have no idea how to get it back so I'm left to simply fiddle without ever actually getting the result I want. Is there a keystroke I'm missing?

I'm not quite sure what you mean. The first time around the only graph you get that is not shown later is the boost preview graph. When you have completed your run through putting together engine and car you get all the help graphs that let you fine-tune things. There is an arrow to the middle left of the screen that lets you open and close these graphs when they are available.

So perhaps this is because I know so little about engine design right now. I put together an engine with a turbo, hit run and the engine freaked out and broke. Usually how it starts for me. From here it switches the original charts with the one that shows the red-yellow-green screen and you go through fine tuning. The problem is, I actually don't know how to build an engine from the beginning so when I put it together it's a guess and when I find out that it did in fact explode I can't get back to the screen that shows the original set of graph since all I can see is the red-yellow-green display. The same goes for the tires, brakes and so on. Since I don't know anything to start, I was wondering if there was a way to switch between the fine tuning display and the original set of graphs after you press the "test" button. Maybe I can include screen shots to present my question better.

There is no way of bringing up the graphs while the engine or car is not completed yet because that is a requirement for the graphs to be shown. The content of the graphs needs a completed engine/vehicle to be calculated.
Not building an engine that explodes should be in the realm of possibilities if you've gone through the tutorial scenarios and understood the concepts presented there. Did you do that?

Is the old blue and red boost graph still available? How do we view that? The left button only switches between engine view and the torque/power/efficiency and engine health graphs.

The blue/red curve boost preview graph is only available when the engine is not complete yet. It doesn't make much sense to display a preview when you can view the full thing the preview is based on quite many assumptions, which don't make any sense to show when you don't have to assume anything anymore.

How do you view the full thing? The only boost graph I see is yellow line sharing the graph with the green efficiency line.

What do you mean by full thing? As soon as you have the full engine, you don't get the preview anymore but the actual numbers with the actual boost and the economy.

I mean the graph that shows the potential boost and the current boost (the video in the tutorial)

But you can now see how it effects engine output directly...

at first you will be presented with the turbo efficiency graph in relation to the engine displacement, this is useful for a prototype turbo so you can quickly judge how the engine would behave... after you finish designing the engine , the turbo designer will then switch over to the engine power graph and you'll be able see exactly how the various settings of the turbo would affect the engine's power band. i find this miles better than guessing how it will behave from the turbo efficiency graph alone.