On the minutes, yes, the standard plan runs 300 minutes per month. The exception comes during the holiday season. In November and December the Bureau of Prisons increases the allotment to 400 minutes to account for the higher volume of family calls during that time of year. That extra hundred minutes makes a real difference during the stretch of the year when staying connected matters most.
On computers, federal facilities do have them, but they are not the open internet access most people picture. Inmates have access to terminals that connect to a limited internal system. Through those terminals they can check their commissary account balance, manage their phone account, and access CorrLinks, which is the Bureau of Prisons approved email messaging system that allows inmates to send and receive messages with approved contacts on the outside.
CorrLinks is worth setting up if you have not already. It allows written communication that goes back and forth faster than physical mail, and it gives your person a way to reach out in between phone calls without burning minutes. Both parties need an account and the inmate has to initiate the connection request from their end first.
The computers are not available around the clock and access is scheduled, but they are a legitimate and regularly used part of how federal inmates stay connected and manage their accounts from inside.