Hey, thanks so much for taking a look! The tutorial has definitely seen some changes since before the jam started so I'd expect confusion if you came into like half of the tutorial then and the whole thing now.
The keyboard controls in indirect mode are somewhat of a relic and don't work quite as I'd like. They are always horizon-relative, even if the camera is aligned to the ship, and can overshoot the top and bottom of the worldspace and thus invert. In the next update I will remove this functionality and make a clearer and easier to understand distinction between just Keyboard mode (direct mode) and Mouse mode (indirect mode). Since mouse indirect control doesn't suffer from this inversion and camera relation issue it should work much better. I'll also look into making it so that swapping to indirect mode maintains your current heading.
As for telling which side of ships is up or down, all ships have a visual design that has reflective golden plating on one side ("top") and grey high frequency greeble particles on another side ("down"). This was done to address the issue you describe!
Trail length does scale with speed, but since the ships have a good amount of momentum, the trail doesn't "update" immediately. There's also a bar at the bottom of the UI labeled "THRT" that shows whether you're thrusting or not.
Locking onto enemies can be disorienting but you can still rotate the camera position around your ship using the normal camera rotation controls to get it back into view. This (and locking itself) are things I consider "advanced" features so the tutorial doesn't address them in its limited time and space, but maybe it should, I'll look into it.
The reason pressing space during tutorial popups unpauses and turns the screen to grey is because space swaps to the overview mode, which uses a grey plate as a transition animation. Since time is slowed greatly during tutorial popups, this transition also takes more time. I've not yet found an elegant solution to this problem apart from disabling the overview mode during tutorial popups, which has lead to complaints in the past. I'll make sure to push a changenote if and when I find a way to handle slowmotion and the overview transition better though!
Again thanks so much for taking a look, I hope you come back and play some more and I'll get to implementing some of the things you mentioned right away!