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You can. But not on a top-solid platform. 

Since in contra games that's typically how you jump down from top-solids. However unlike Contra games pressing down usually makes your character go in prone position(which in this game is assigned to different button) before you jump down, in this game it just makes you aim down which wasn't a thing unless you jumped or you're holding the 'R' button for Contra 3.

I was debating whether or not to have some accessibility options for the controls, like making them configured like Contra 3's where aiming down from a stand still required another button input. Or making the crouch button be a valid button to jump down from top-solids instead of pressing down. But never got around to doing so.

No Crisis Flash(aka the red flash that indicates enemy attacks) really screws me over, you just hafta feel out the attacks. Though its nice you highlight the projectiles, it's just that I wish there was a way to distinguish between projectiles that hit you and the projectiles that will miss you. The Time Crisis games usually highlight slow-moving(non-hitscan) projectiles with an Orange tracer on top of them being able to shot mid-air.

Defeated Sakuya in the third attempt. (my spam-clicking too stronk lol)

Accessing the options menu from in-game doesn't work, I can't click on any of the options. But other than that the game runs smoothly.