What exactly is a 20 amp dedicated line?

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is the NEC the National Electrical Code?

Yes.

Second, if a multi wire branch circuit is set up in the manner I described above, please explain how a multi pole branch circuit breaker works.

The multi pole breaker has the function of controlling all of the circuits of a multi wire branch circuit simultaneously. NEC Code changes mandated that all circuits of a multi wire branch must be de-energized by a one handle action. All on or all off. Pre-code change, individual single pole breakers were used. It is a safety thing for an electrician or maintenance person that may be working on one or more of the circuits of the multi wire branch circuit.

In commercial and industrial buildings 3 phase 4 wire multi wire branch circuits are quite common.
(3) hots, (1) neutral, and (1) equipment ground.

For example, if each hot energizes a separate receptical, is it possible that a short or overload of one receptical fed by one hot would NOT trip the breaker for the other circuit fed by the other hot?

That is true where a single pole breaker is used for each circuit of a multi wire branch circuit.
That is not the case when a multi pole breaker is used. In the case of a 3ph 4 wire multi wire branch circuit a 3 pole breaker must be used for the overcurrent protection of the branch circuit.

If one of the circuits of the three was overloaded the breaker will trip open and take the other two circuits with it.

Multi wire branch circuits are a thing of the past now..... At least in jurisditions that approved that part of NEC.

now the really important question is what's a Porter port? Drawing a slack jawed zero over here!

If you are trying to get 2 dedicated lines with one romex I'm assuming he is speaking of using 12/3 with ground. or 10/3 ...(same)...If you keep each hot on the same Phase in the Main Elect. panel then at your point of contact to your receptacle (in the J-box, at the stereo) there would be no way of accidentally ending up with 220 volts. Wiring is No Hobby, Call a professional. And I'm not trying to be a smart-ass with that comment either...