360 Aiming in Top-Down Shooter (Hotline Miami clone)

Easiest is probably using the built-in physics race-car movement,
will handle angles for you,
while shooting can just be:

on fire 1
>>> shoot "bullet" at speed xxx - use direction of "character"

Best looking, precise and complete solution would probably involve using some trigonometry.

To rotate the player and let him face the mouse (or crosshair) you have two choices:

builtin way:
set angle to OAngle("player", "xmouse", "ymouse")

best way:
set angle to ATan2(Y( "player" ) - ymouse, xmouse - "player" ) )

In the first one I included some extra "quotes" for xmouse and ymouse, maybe this led to your troubles, sorry!

The second one will show its additional potential on further distances,
since it will give you floating point precision,
while the OAngle function only returns integer values.

But they work quite the same on smaller distances.

The Atan2 notation calls the "arctangent" mathematic function,
an inverse trigonometric function that will give you the angle between a horizontal X axis and the vector between two points,
here we have specified the two points being your player's X,Y and the mouse X,Y position.

If you're using set angle to OAngle("Player", xmouse, ymouse)
The result can be 33

With set angle to ATan2(Y( "Player" ) - ymouse, xmouse - "Player" ) )
The result can be 33.7299

The float values bring accuracy to the table. So for perfect accuracy use the second method.

Assuming you're using the Atan2 method,
you probably have to setup a precise method for "directing" the shoot
(the builtin "shoot in direction of..." just aims in limited range of directions)

You may check this bullet example (second post):
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main focus here was on collision, but it also embeds correct aiming at crosshair like you need

check the "fastloop bullet" group!

I think you will notice a bigger difference in results the longer the distance of the bullet travels. So doing some target practice testing up close you can't see a difference, but taking long shots you could.

Easiest solution is always the best,
we sometimes tend to overcomplicate things XD

The physics movement is a great idea! To step in late here: I made a Please login to see this link. the other day using 360-degree movement/rotations in case you're curious about that. It uses floats (decimal points) so that the projectiles always move precisely toward the target regardless of distance.

Very cool example Snail!

This other example I was referring was targeting (and colliding) with floating precision too >:)
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(maybe lower "speed" value of the bullet object to see better..)

but I guess muskalator was happier with an equally-good-looking-but-easier-to-handle solution XD

I would just note that using the physics movements for bullets will have poor performance results on the mobile runtimes..