When exaclty does the US enters at war&war time income questoins

@Gallo:

Since the Collecting Income phase is at the end of the turn, that means the US can not start performing any hostile action (either combat movement, or non-combat movement that go beyond their pace time allowed movenments) until its 4th Turn.
Am I right about this?

Secondly: the US starts cashing its war time income at its 3rd Turn collecting income phase (so it will have a lot of money to buy new stuff at the beggining of next turn (4th) when at full war). Am I correct

Correct.

@Gallo:

Thirdly:
how much $ does the US makes while not at war?
how much $ does the US makes when at war?

52 IPCs when not at war.  When at war (and controlling all original territories), 82 IPCs in the box rules and 77 IPCs in Alpha+.2.

@Gallo:

If (say) at 3rd turn the US decides to declare war against Japan (but not Germany) or Germany/Italy (but not japan), I assume the US remains neutral bis-a-bis the powers didn’t declared war too… in such case: does the US claims all its income boost or only part of it. how much?

The US gets all of its NOs if it’s at war with any Axis power.

@Gallo:

From the manual: if not yet at war, the US can declare war to some or all Axis Powers at the beggining of Collencting Income phase its 3rd turn.

Since the Collecting Income phase is at the end of the turn, that means the US can not start performing any hostile action (either combat movement, or non-combat movement that go beyond their pace time allowed movenments) until its 4th Turn.
Am I right about this?

Correct.

@Gallo:

Secondly: the US starts cashing its war time income at its 3rd Turn collecting income phase (so it will have a lot of money to buy new stuff at the beggining of next turn (4th) when at full war). Am I correct

Correct
@Gallo:

Thirdly:
how much $ does the US makes while not at war?
how much $ does the US makes when at war?

When not at war 52 IPC’s.
When at war, the USA gets 77 right away, if they take some key islands right away that gets bumped to 82.  However it Japan attacks Phillipines and Hawaii on J3 and takes them as an example USA will only start with 67.
@Gallo:

If (say) at 3rd turn the US decides to declare war against Japan (but not Germany) or Germany/Italy (but not japan), I assume the US remains neutral bis-a-bis the powers didn’t declared war too… in such case: does the US claims all its income boost or only part of it. how much?

thanks in advance!

I think the when the USA declares it is on all, and they dont’ have a choice to stay neutral in one theatre.  Some confirm this part.

Yeah the income is from National Objectives.  It is the same in Pacific, only there it is a flat rate increase, rather than being split into 5.