In my experience, they don't take "requests" but with older inmates, there are some considerations like getting the bottom bunk.

Restrictive housing is 'solitary confinement', and can be classified as "Administrative Segregation" or "Disciplinary Segregation" which to every inmate is known as, "The Hole" or the SHU (Special Housing Unit). Inmates in the SHU are allowed ONE 15-minute phone call PER WEEK.

I wouldn't say "most", but there are many people on the outside who like to communicate with inmates, for some reason... but if you suspect your inmate is, you're probably right

Within the first week of completed orientation 

2-3 days, but be mindful that the distribution of the mail to the innmates is up to the correctional officers who run the mailroom

the staff gives them a slip of paper with the amounts deposited into their inmate account

yes

it's immediate

yes, but you would have to do this with prior-permission and make the exchange of the ring in the visiting room.

you need to think hard because this is not going to be easy if you go through with it... it sounds like you've already figured it out...