WHAT IS THE PURPOSE OF THE BARRACKS

It does not need a recruitment office. It speeds up infantry recruitment by 50% per level (theres two levels). Its biggest use is the allowance to produce calv (Calvary), that is baracks paired with a workshop. As afore stated it does increase infantry recruitment but in order for that to take place you need a recruitment office, However a recruitment office is not required, to actually build the baracks

okay,

barracks is only for speeding recruitment and unlocking Cav.

Q: Scenario - recruitment office disable

1. is the barrack recruitment still on going?

2. at what speed?

3. is the recruitment speed of the barracks tied to recruitment office?

Barracks works better on double provinces, and thus even faster infantry recruitment. as far as doing the numbers on everything you can see how long it takes for infantry recruitment, you can also play with it and turn barracks on and off and see the time difference, thats what i do every so often

yes no recruitment office/disabled recruitment office = no increased recruitment speed you can still produce artys but no positive recruitment speed in fact theres zero recruitment period

PLAYtoWIN

However a recruitment office is not required, to actually build the baracks

It is incorrect. You DO need a RO to build a barracks.

However a barracks does still work without a RO (just as a significantly decreased speed)