Assume that I’m a former President or VP. Can I set up a SCIF at wherever I’m living, and would it have a sort of “desk clerk” to monitor who goes in and comes out to ensure nothing important walks away or is it on the honor system?
Former presidents and VPs have no clearance. They have no need for a SCIF.
So if they needed to advise the current President on something, they’d need to be cleared and a SCIF sort of installed in their house, or what have you?
A SCIF is commissioned and certified by the Government, not by the individual or organization that needs to use it. If a SCIF is needed in order for an individual to do work for Government needs, then one can be constructed and certified in appropriate locations. If a SCIF were to be constructed so private citizen could work for the Government on something that required access to SCI, then it would need to be operated according to the security rules for that particular program. Sometimes, that requires that when he SCIF is open and in use there is someone outside the SCIF, monitoring it. Sometimes this might not require a monitor as long as the person using the SCIF is also the “custodian” of the SCIF.
“It is common for outgoing presidents and officials to be ‘read in’ on issues and topics where their prior position and expertise are useful. This is at the discretion of the current sitting president.”
I can’t really seem to find a reputable source for this, but all the stories about Trump not receiving classified information after leaving office all agree it’s normal for that to happen. How exactly that happens or how that information is kept secure I can’t seem to find anywhere.
Why would a SCIF be needed? Classified stuff can be discussed outside of a SCIF. Documents can be carried outside of a SCIF. Secure mobile phones are another option. Not to mention the fact that he could just be provided with a laptop capable of remote access to a classified network. VPN access to SIPRNET is damn near routine, and even JWICS is remotely accessible. A person with the proper access and need is able to access all the classified data they require from the comfort of their living room.
For Top Secret information maybe, but for anything with an SCI designation I thought the terminal must still be in a SCIF.
For the vast majority of classified information a SCIF is not required, only for information with an SCI designation. The SCI designation can be put onto any level of classification (i.e., Confidential/SCI and Secret/SCI as well as TS/SCI).
You are right. SCI (and SAP/SAR) information can only be viewed or worked on within an appropriate classified facility. Computers for that level of information are either isolated to that area or only connected to a secure network authorized to carry that classification of data.
All true - though there are specific requirements about, for example, how such documents may be transported and must be secured. Taking them to your home office is not permissible, in general.
Discussion, for example, is supposed to be done only on a secured phone, and you are expected to to be situationally aware so you don’t, say, chat about the nuclear wessels at Alameda in the middle of a Starbucks.
SCI (and SAP) has separate and more stringent procedures and policies than Secret (S) or Top Secret (TS). Some call it “above Top Secret”, but it is really, just separate, with separate security requirements. For example, the DoD Manual 5200.01 (DoD Information Security Program: Protection of Classified Information) has this to say about information systems and SCI:
a. SCI. SCI, regardless of classification level, must be processed only on an information system accredited for SCI processing (e.g., Joint Worldwide Intelligence Communications system (JWICS)). It may not be processed on, transferred to, or stored on SIPRNET, even if the information is SECRET//SI, SECRET//HCS, etc., as SIPRNET is not accredited for SCI. Any transfer to and/or processing of SCI on SIPRNET constitutes a data spillage from a higher to a lower-security information domain, in accordance with Reference (bt).
In my experience (SCI security policies are compartment by compartment, so no one can speak definitively), discussions occur only in an authorized SCIF, electronic communications are restricted to authorized computers and networks, transporting information physically requires authorized couriers.
I thought SIPRNET and JWICS were airgapped. Is that not true?
Nice try, China. 
For real. I would think that cracking a VPN would be a lot simpler than defeating an airgapped system.