I need an exact definition of end-on-end and back-to-back ticketing, where the former is permitted by some fare rules and the latter is strictly prohibited.

In the below examples, HKG/SZX and BJS/TSN are two distant city pairs, and in each pair the two cities are very close to each other such that no regular air transportation is possible, but are still considered different cities.

Assume that all round-trip fares have a Saturday-night requirement, allows end-on-end and double open jaws.

The following is a classical prohibited back-to-back ticketing, where the traveller book two round-trip fares and use the segments in chronological order:
Ticket AA:
2018-01-01 HKG-BJS
2018-01-10 BJS-HKG
Ticket AB:
2018-01-03 BJS-HKG
2018-01-08 HKG-BJS

However, if we make all 4 segments into a single booking, can't the reservation system treats the journey as an end-to-end combination?
Ticket B:
PU B1:
FC B11 (HKG-BJS round-trip fare): 2018-01-01 HKG-BJS
FC B12 (BJS-HKG round-trip fare): 2018-01-10 BJS-HKG
PU B2:
FC B21 (BJS-HKG round-trip fare): 2018-01-03 BJS-HKG
FC B22 (HKG-BJS round-trip fare): 2018-01-08 HKG-BJS
Can this ticket be constructed by using the above rules?

Moreover, if the traveller intends to circumvent the minimum stay requirement, and book the following air tickets, does it constitute the prohibited practice of back-to-back ticketing:
Ticket CA:
2018-01-01 HKG-BJS
2018-01-10 BJS-HKG
Ticket CB:
2018-01-03 BJS-SZX
2018-01-08 SZX-BJS
The traveller's home is about the same distance between HKG and SZX. Both airports are equally convenient.

How about the following variants then:
Ticket DA:
2018-01-01 HKG-BJS
2018-01-10 BJS-SZX
Ticket DB:
2018-01-03 BJS-HKG
2018-01-08 SZX-BJS
or any combinations by substituting HKG with SZX or vice versa and the traveller is doing these flights every two weeks with the frequent flyer account applied, with different combinations of HKG/SZX substituting each other in different tickets?

In the following examples, the traveller books the segments of two weeks all on a single ticket:
Ticket E:
2018-01-01 HKG-BJS
2018-01-03 BJS-SZX
2018-01-08 SZX-BJS
2018-01-10 BJS-HKG

Ticket F:
2018-01-01 HKG-BJS
2018-01-03 BJS-SZX
2018-01-08 HKG-BJS
2018-01-10 BJS-SZX

Ticket G:
2018-01-01 HKG-BJS
2018-01-03 BJS-HKG
2018-01-08 SZX-BJS
2018-01-10 BJS-SZX

Ticket H:
2018-01-01 HKG-BJS
2018-01-03 BJS-SZX
2018-01-08 SZX-BJS
2018-01-10 BJS-SZX

Ticket I:
2018-01-01 HKG-BJS
2018-01-03 BJS-HKG
2018-01-08 HKG-BJS
2018-01-10 BJS-SZX

For tickets E, F, G, H and I, can the round-trip fares requiring Saturday night stay and permitting open jaws and end-on-end used, by combining 2018-01-01 and 2018-01-10 as a PU, and 2018-01-03 and 2018-01-08 as another PU?

Tickets that are purchased in an order to violate minimum stays or other requirements are classic examples. American Airlines offers easy definitions in their examples if prohibited practices in its Conditions of Carriage..

Back-to-back ticketing: The combination of two or more roundtrip excursion fares end to end for the purpose of circumventing minimum stay requirements.

Throwaway ticketing: The usage of roundtrip excursion fare for one-way travel.

Hidden city / point beyond ticketing: Purchase of a fare from a point before the passenger's actual origin or to a point beyond the passenger's actual destination.

Duplicate and impossible/illogical bookings: Duplicate or impossible/illogical American Airlines bookings are prohibited without prior authorization from American Airlines. A duplicate or impossible/illogical booking includes, but is not limited to, bookings for the same passenger on flights traveling on or about the same date between one or more of the same or nearby origin and/or destination (such as JFK to DFW and LGA to DFW or DFW to LAX and DFW to ONT), or bookings with connections that depart before the arrival of the inbound flight.

Fraudulent, fictitious and abusive bookings: Fraudulent, fictitious and/or abusive bookings are prohibited. These types of bookings are defined as any bookings made without having been requested by or on behalf of the named passenger. Additionally, creating bookings to hold or block seats for the purpose of obtaining lower fares, AAdvantage award inventory, or upgrades that may not otherwise be available, or to gain access to airport facilities, or to circumvent any of American Airlines' fare rules or policies, is prohibited without prior authorization from American Airlines.

(An example if the last example might be making a booking to enter an airside lounge, and cancelling after entering.)