Intake and assignment can be quick if they were transferred within the same prison system. However, across agencies, the processing could take up to two weeks before visitation and phone privileges are restored.

there is no time frame. they are locked up and they don't need to transfer them until the next court date

Inmates are allowed to bring a "box" with any item they purchased or were sent to them that is in their possession at the time of transfer. Shoes, clothing, reading material, pictures, personal etters or hygiene products are within that list of acceptable 'box items'.

Most inmates on transfer might spend a night or a week in the SHU awaiting a bed in the facility. The situation you are referring to is called "separatee", where two inmates are either co-defendants OR "they know each other" and are required to be segregated. There are two types of segregation outlined by the Bureau of Prisons: disciplinary and administrative detention. This one is administrative.

he will have to wait at least 6 months before he can ask for a transfer.

They do not notify anyone before coming and collecting an inmate for transport. All inmate movement is kept confidential for the safety of the transporting guards.

If they are approved and awaiting transfer it depends on the bed space available in the treatment dorm

Yes, you should wait until they are confirmed at their permanent housing unit to send anything. There is no address for "In Transit".

Only items purchased through the commissary AND all personal mail, legal documents or writings. 

When the CO says "pack your stuff", you throw everything into a big plastic bin. You are allowed to take everything in your locker, including all of the commissary items you have bought.