So I know that obstinance is continuing in sin, but does it apply to all sin (mortal and venial) or just continuing in mortal sin? For example: if I commit a venial sin, know it is one, and keep doing it, is that obstinacy?
It is not continuing to sin, although that is a part of it. It is the refusal to be corrected, the refusal to be educated or the refusal to obey. All of us are repeat offenders of our own areas of sinfulness, but we are constantly trying to obey.
Obstinacy would be the person who decides that abortion is acceptable and despite all Church teaching to the contrary, will not change. Some politicians have recently been excommunicated for voting in favor of abortion. They refused to change their voting despite being told to do so by the bishops.
I suppose this could pertain to any matter of of the faith, although it is a part of what qualifies a sin to be mortal- that knowing it to be a serious wrong, you commit it anyway. Venial sins are not “serious” and are not made serious by obstinacy, but the obstinacy itself could be a mortal sin.
Slow to learn, refusal to learn.