Just a necessary clarification I've not found anywhere - can you split a Full Action in two Rounds so like you shoot, begin to reload with a Full Action, finish reloading the next turn and take a Half Aim?

Sure as long as you don't repeat the same action twice, such as shooting, in the same round...

I was asking myself the same.
In my example it was the aim action.

Can you shoot, aim - aim, shoot and get the bonus for full round aim for the second shot?

Well, even if the rules don't state that you can, you can use that as a useful home rule After all, you can kill someone while he reloads or aims. Are there any issues with it that I don't see?

I am not totally sure, but I don't think you are allow to split the aim action itself over two turns (you can aim one turn and then shoot... as long as you do nothing else between). So you could Shoot/Aim and then Shoot/Aim (bad way to do it though), or Full action Aim and then Shoot, but (as far as I can remember) you can't do Shoot/Aim and then Aim/Shoot to get a +20 (you would get a +10 and would have wasted half an action).

I may be wrong, but I am fairly sure about that. Obviously if you house rule it that way that's fine.

Doesn't the Aim action stack multiple times up to a certain threshold? Even if you could not split a Full Action in two Half Actions by RAW, you could do two Half Action Aims in succession to get the same result, couldn't you?

Granted, this doesn't really help for solving the core question as "Aim" is (iirc) the only action that explicitly says it can be used in Full as well as Half Action, but still ...

Other than that, I would agree with Virtus. Rounds are only an abstraction of real time, and if one round is 6 seconds, there's nothing that should prevent anybody from doing X in 12, 18 or 24 seconds regardless of sequence, as long as the "split actions" stay connected. Obviously, this could also result in "interruptions" - when somebody gets hit whilst aiming or reloading, I would expect him to loose the half action already "invested". When hit whilst reloading he could even drop the ammunition to the ground, requiring the character to pick it up again once it's his turn.

I have allowed such things in my game with a few exceptions, here is one.

I had a player shoot at a point blank target then he wanted to aim for the next shot. I allowed it but then he was engaged in melee on his opponets turn and was forced to dodge. This caused him to loose any aim he had. This is obvious to most I would think as it is common sense, but he was upset having lost a half action. Just something to consider.