To the first question. Using "der" in this context would be inappropriate, as it suggests singular: on the other Hand would "dieser" suggest the choice of one element from a variety of others, which would be inappropriate with a single dog.
"Dieser" is often combined with a complement like "jener" to show a duality in between the chosen elements.
Ich habe zwei Hunde. Dieser / Der eine ist ein Labrador-Mischling,
jener / der andere ist ein Terrier.
When referring to positional elements or previously mentioned subjects, dieser refers to the closer (in location or text)
Jan mag Cola. Georg mag Pepsi. Dieser (Georg) mag Computerspiele, jener (Jan) mag sie nicht.
In brackets is the explicit naming of the referred subject.
Hier stehen zwei Säulen. An dieser (der näheren) klebt ein Plakat.
When using "Der" in a sense of "Dieser" this is normally accomplished by pointing to the referred Subject, as "Der" requires exact definition.
Simply said: Not with "Der" / "Die" / "Das" standing alone. As mentioned in the Answers here and here it is more common in southern Germany, but generally considered bad style, when used with a Name in front of other people.
It gets even worse without a name. That is generaly considered very impolite and sometimes derogative. As @Emmanuel pointed out this form is quite popular in written language to refer to a previosly introduced Person, or when referring to the "position" of a person:
Der Oppositionsvorsitzende warf XY Korruption vor. Der wiederum bestritt den Vorwurf entschieden.
In this case "Der" is referring to the already introduced "party" XY and takes a function similar to "Dieser". Thus it is not derogative or even impolite, oppositely it is good style to evade reusing the same word again and again.
You can of course use "Dieser" / "Diese" / "Dieses", but only when referring to a previosly introduced Person. Sometimes this is done by showmasters introducing their candidates.
Dieser Kandidat hier wettet, dass er einen Traktor auf 2 Rädern durch einen
Hindernisparcours steuern kann.
No in general not. as @wrzlprmft mentioned you should of course emphasise it a little bit, else one could think of "Die Richtung" as some restaurant.
One can of course always add additional stressing to mark you are doing something special, but that is not required.